internlm/Lean-Github · Datasets at Hugging Face

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. apply And.intro . simp . simp	case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t h : r = t ⊢ q ∈ a ∧ t ∈ a	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	apply connectingLine_uniq	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ a = q ⊔ t	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. assumption	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. simp	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. simp	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	apply connectingLine_uniq	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ c = r ⊔ t	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. assumption	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. simp	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. simp	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	simp[collinear]	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ¬collinear t q r	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ∀ (x : line P), (p ⊔ q) ⊓ (r ⊔ s) ∈ x → q ∈ x → ¬r ∈ x
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	intro l htl hql hrl	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ∀ (x : line P), (p ⊔ q) ⊓ (r ⊔ s) ∈ x → q ∈ x → ¬r ∈ x	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ False
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	have l_is_a : l = a := by rw[a_is_q_t] apply connectingLine_uniq <;> assumption	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ False	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l l_is_a : l = a ⊢ False
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	rw[l_is_a] at hrl	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l l_is_a : l = a ⊢ False	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ False
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	have : collinear p q r := by simp[collinear] exists a apply And.intro . simp . apply And.intro . simp . assumption	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ False	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a this : collinear p q r ⊢ False
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	contradiction	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a this : collinear p q r ⊢ False	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	rw[a_is_q_t]	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = a	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = q ⊔ t
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	apply connectingLine_uniq <;> assumption	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = q ⊔ t	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	simp[collinear]	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ collinear p q r	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ ∃ l, p ∈ l ∧ q ∈ l ∧ r ∈ l
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	exists a	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ ∃ l, p ∈ l ∧ q ∈ l ∧ r ∈ l	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a ∧ q ∈ a ∧ r ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	apply And.intro	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a ∧ q ∈ a ∧ r ∈ a	case left P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. simp	case left P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a	case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	. apply And.intro . simp . assumption	case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	rw[a_is_q_t, c_is_r_t, connectingLine_comm]	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear a b c	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear (t ⊔ q) b (r ⊔ t)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	apply dual_triangle	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear (t ⊔ q) b (r ⊔ t)	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear t q r
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle_part	[159, 1]	[232, 13]	assumption	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear t q r	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	intro ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P ⊢ isQuadrangle p q r s → isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	let a := p ⊔ q	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	let b := q ⊔ r	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	let c := r ⊔ s	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	let d := s ⊔ p	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	have triangle_abc : ¬ collinear a b c := by apply dual_quadrangle_part exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	have triangle_abd : ¬ collinear a b d := by apply triangle_rotate apply dual_quadrangle_part apply quadrangle_rotate apply quadrangle_rotate apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	have triangle_acd : ¬ collinear a c d := by apply triangle_rotate apply triangle_rotate apply dual_quadrangle_part apply quadrangle_rotate apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	have triangle_bcd : ¬ collinear b c d := by apply dual_quadrangle_part apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d triangle_bcd : ¬collinear b c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	exact ⟨triangle_abc, triangle_abd, triangle_acd, triangle_bcd⟩	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d triangle_bcd : ¬collinear b c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply dual_quadrangle_part	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ ¬collinear a b c	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle p q r s
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle p q r s	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply triangle_rotate	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear a b d	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear d a b
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply dual_quadrangle_part	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear d a b	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle s p q r
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle s p q r	case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle r s p q
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle r s p q	case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle q r s p
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle q r s p	case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle p q r s
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle p q r s	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply triangle_rotate	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear a c d	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear d a c
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply triangle_rotate	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear d a c	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear c d a
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply dual_quadrangle_part	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear c d a	case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle r s p q
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle r s p q	case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle q r s p
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle q r s p	case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle p q r s
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle p q r s	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply dual_quadrangle_part	P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ ¬collinear b c d	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle q r s p
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	apply quadrangle_rotate	case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle q r s p	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle p q r s
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_quadrangle	[234, 1]	[266, 65]	exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩	case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle p q r s	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	ProjectivePlane.dual_involution	[281, 1]	[283, 19]	rfl	P L : Type p q r s : P h : ProjectivePlane P ⊢ let h' := inferInstance; h' = h	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	Fano.Fano.quadrangle1236	[383, 1]	[384, 83]	simp[collinear]	P L : Type ⊢ ¬collinear Points.p1 Points.p2 Points.p3	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	Fano.Fano.quadrangle1236	[383, 1]	[384, 83]	simp[collinear]	P L : Type ⊢ ¬collinear Points.p1 Points.p2 Points.p6	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	Fano.Fano.quadrangle1236	[383, 1]	[384, 83]	simp[collinear]	P L : Type ⊢ ¬collinear Points.p1 Points.p3 Points.p6	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	Fano.Fano.quadrangle1236	[383, 1]	[384, 83]	simp[collinear]	P L : Type ⊢ ¬collinear Points.p2 Points.p3 Points.p6	no goals
https://github.com/loewenheim/projective-plane.git	7ade52678ac3df537f38d04de46db9aca752f3ca	ProjectivePlane.lean	Fano.Fano.point_line_uniq	[386, 1]	[387, 9]	decide	P L : Type ⊢ ∀ {p q : Points} {l m : Lines}, p ∈ l → q ∈ l → p ∈ m → q ∈ m → p = q ∨ l = m	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	intro v vars	⊢ ∀ (v : String) (vars : List String), v ∈ vars → String.length v ≤ max_var_name vars	v : String vars : List String ⊢ v ∈ vars → String.length v ≤ max_var_name vars
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	induction vars with \| nil => intro hm exact absurd hm (List.not_mem_nil v) \| cons x xs ih => intro h rw [List.mem_cons] at h cases h with \| inl hvx => unfold max_var_name conv => rhs; rw [← hvx] apply Nat.le_max_left \| inr hvxs => unfold max_var_name calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right	v : String vars : List String ⊢ v ∈ vars → String.length v ≤ max_var_name vars	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	intro hm	case nil v : String ⊢ v ∈ [] → String.length v ≤ max_var_name []	case nil v : String hm : v ∈ [] ⊢ String.length v ≤ max_var_name []
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	exact absurd hm (List.not_mem_nil v)	case nil v : String hm : v ∈ [] ⊢ String.length v ≤ max_var_name []	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	intro h	case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs ⊢ v ∈ x :: xs → String.length v ≤ max_var_name (x :: xs)	case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v ∈ x :: xs ⊢ String.length v ≤ max_var_name (x :: xs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	rw [List.mem_cons] at h	case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v ∈ x :: xs ⊢ String.length v ≤ max_var_name (x :: xs)	case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v = x ∨ v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	cases h with \| inl hvx => unfold max_var_name conv => rhs; rw [← hvx] apply Nat.le_max_left \| inr hvxs => unfold max_var_name calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right	case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v = x ∨ v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	unfold max_var_name	case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ max_var_name (x :: xs)	case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	conv => rhs; rw [← hvx]	case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)	case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length v) (max_var_name xs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	apply Nat.le_max_left	case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length v) (max_var_name xs)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	unfold max_var_name	case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)	case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right	case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Fol.lean	max_var_name_mem	[399, 1]	[418, 83]	apply Nat.le_max_right	v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ max_var_name xs ≤ Nat.max (String.length x) (max_var_name xs)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	intro p inp	⊢ ∀ (p : Char → Bool) (inp : List Char), List.length (lexwhile p inp).snd ≤ List.length inp	p : Char → Bool inp : List Char ⊢ List.length (lexwhile p inp).snd ≤ List.length inp
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	induction inp with \| nil => simp [lexwhile] \| cons c cs ih => simp [lexwhile] cases p c <;> simp exact Nat.le_succ_of_le ih	p : Char → Bool inp : List Char ⊢ List.length (lexwhile p inp).snd ≤ List.length inp	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	simp [lexwhile]	case nil p : Char → Bool ⊢ List.length (lexwhile p []).snd ≤ List.length []	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	simp [lexwhile]	case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p (c :: cs)).snd ≤ List.length (c :: cs)	case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (if p c = true then (String.append (Char.toString c) (lexwhile p cs).fst, (lexwhile p cs).snd) else ("", c :: cs)).snd ≤ Nat.succ (List.length cs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	cases p c <;> simp	case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (if p c = true then (String.append (Char.toString c) (lexwhile p cs).fst, (lexwhile p cs).snd) else ("", c :: cs)).snd ≤ Nat.succ (List.length cs)	case cons.true p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p cs).snd ≤ Nat.succ (List.length cs)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Parser.lean	lexwhile_monotonic	[35, 1]	[42, 31]	exact Nat.le_succ_of_le ih	case cons.true p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p cs).snd ≤ Nat.succ (List.length cs)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	intro l1 l2	α : Type inst✝¹ : Ord α inst✝ : BEq α ⊢ ∀ (l1 l2 : List α), List.length (merge l1 l2) = List.length l1 + List.length l2	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge l1 l2) = List.length l1 + List.length l2
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	match l1 with \| .nil => unfold merge; rw [List.length_nil, Nat.zero_add] \| .cons h1 t1 => unfold merge match l2 with \| .nil => simp only [List.length_cons, List.length_nil, Nat.add_zero] \| .cons h2 t2 => simp only [List.length_cons] split . rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega . rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge l1 l2) = List.length l1 + List.length l2	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	unfold merge	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge [] l2) = List.length [] + List.length l2	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length l2 = List.length [] + List.length l2
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	rw [List.length_nil, Nat.zero_add]	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length l2 = List.length [] + List.length l2	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	unfold merge	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (merge (h1 :: t1) l2) = List.length (h1 :: t1) + List.length l2	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match l2 with \| [] => h1 :: t1 \| l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length l2
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	match l2 with \| .nil => simp only [List.length_cons, List.length_nil, Nat.add_zero] \| .cons h2 t2 => simp only [List.length_cons] split . rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega . rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match l2 with \| [] => h1 :: t1 \| l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length l2	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	simp only [List.length_cons, List.length_nil, Nat.add_zero]	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match [] with \| [] => h1 :: t1 \| l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length []	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	simp only [List.length_cons]	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (match h2 :: t2 with \| [] => h1 :: t1 \| l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length (h2 :: t2)	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (if isLE (compare h1 h2) = true then h1 :: merge t1 (h2 :: t2) else h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	split	α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (if isLE (compare h1 h2) = true then h1 :: merge t1 (h2 :: t2) else h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2) case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	. rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2) case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	. rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	rw [List.length_cons, merge_length t1 (h2 :: t2)]	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + List.length (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	simp only [List.length_cons]	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + List.length (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + Nat.succ (List.length t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	omega	case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + Nat.succ (List.length t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	rw [List.length_cons, merge_length (h1 :: t1) t2]	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (List.length (h1 :: t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	simp only [List.length_cons]	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (List.length (h1 :: t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (Nat.succ (List.length t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Common.lean	Set.merge_length	[105, 1]	[121, 14]	omega	case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (Nat.succ (List.length t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	intro t	α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ ∀ (tr : Trail α), List.length (backtrack tr) ≤ List.length tr	α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α t : Trail α ⊢ List.length (backtrack t) ≤ List.length t
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	induction t with \| nil => unfold backtrack; apply Nat.le_refl \| cons d ds ih => simp [backtrack] cases d.decision == .Deduced . simp . simp; apply Nat.le_succ_of_le; assumption	α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α t : Trail α ⊢ List.length (backtrack t) ≤ List.length t	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	unfold backtrack	case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length (backtrack []) ≤ List.length []	case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length [] ≤ List.length []
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	apply Nat.le_refl	case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length [] ≤ List.length []	no goals
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	simp [backtrack]	case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (backtrack (d :: ds)) ≤ List.length (d :: ds)	case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if (d.decision == LitState.Deduced) = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)
https://github.com/benjaminfjones/reckonlean.git	8768f7342ba226cfc2d7b92e47432f1da66eff25	ReckonLean/Dpll.lean	length_backtrack	[195, 1]	[204, 50]	cases d.decision == .Deduced	case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if (d.decision == LitState.Deduced) = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)	case cons.false α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if false = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds) case cons.true α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if true = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. apply And.intro . simp . simp

case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t h : r = t ⊢ q ∈ a ∧ t ∈ a

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

apply connectingLine_uniq

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ a = q ⊔ t

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. assumption

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. simp

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ q ∈ a case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. simp

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t ⊢ t ∈ a

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

apply connectingLine_uniq

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ c = r ⊔ t

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. assumption

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ≠ t case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. simp

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ r ∈ c case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. simp

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t ⊢ t ∈ c

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

simp[collinear]

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ¬collinear t q r

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ∀ (x : line P), (p ⊔ q) ⊓ (r ⊔ s) ∈ x → q ∈ x → ¬r ∈ x

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

intro l htl hql hrl

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t ⊢ ∀ (x : line P), (p ⊔ q) ⊓ (r ⊔ s) ∈ x → q ∈ x → ¬r ∈ x

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ False

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

have l_is_a : l = a := by rw[a_is_q_t] apply connectingLine_uniq <;> assumption

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ False

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l l_is_a : l = a ⊢ False

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

rw[l_is_a] at hrl

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l l_is_a : l = a ⊢ False

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ False

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

have : collinear p q r := by simp[collinear] exists a apply And.intro . simp . apply And.intro . simp . assumption

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ False

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a this : collinear p q r ⊢ False

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

contradiction

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a this : collinear p q r ⊢ False

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

rw[a_is_q_t]

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = a

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = q ⊔ t

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

apply connectingLine_uniq <;> assumption

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ l ⊢ l = q ⊔ t

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

simp[collinear]

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ collinear p q r

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ ∃ l, p ∈ l ∧ q ∈ l ∧ r ∈ l

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

exists a

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ ∃ l, p ∈ l ∧ q ∈ l ∧ r ∈ l

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a ∧ q ∈ a ∧ r ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

apply And.intro

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a ∧ q ∈ a ∧ r ∈ a

case left P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. simp

case left P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ p ∈ a case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a

case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

. apply And.intro . simp . assumption

case right P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t l : line P htl : (p ⊔ q) ⊓ (r ⊔ s) ∈ l hql : q ∈ l hrl : r ∈ a l_is_a : l = a ⊢ q ∈ a ∧ r ∈ a

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

rw[a_is_q_t, c_is_r_t, connectingLine_comm]

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear a b c

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear (t ⊔ q) b (r ⊔ t)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

apply dual_triangle

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear (t ⊔ q) b (r ⊔ t)

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear t q r

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle_part

[159, 1]

[232, 13]

assumption

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r left✝¹ : ¬collinear p q s left✝ : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s t : P := a ⊓ c t_is_not_q : q ≠ t t_is_not_r : r ≠ t a_is_q_t : a = q ⊔ t c_is_r_t : c = r ⊔ t triangle_tqr : ¬collinear t q r ⊢ ¬collinear t q r

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

intro ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P ⊢ isQuadrangle p q r s → isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

let a := p ⊔ q

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

let b := q ⊔ r

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

let c := r ⊔ s

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

let d := s ⊔ p

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

have triangle_abc : ¬ collinear a b c := by apply dual_quadrangle_part exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

have triangle_abd : ¬ collinear a b d := by apply triangle_rotate apply dual_quadrangle_part apply quadrangle_rotate apply quadrangle_rotate apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

have triangle_acd : ¬ collinear a c d := by apply triangle_rotate apply triangle_rotate apply dual_quadrangle_part apply quadrangle_rotate apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

have triangle_bcd : ¬ collinear b c d := by apply dual_quadrangle_part apply quadrangle_rotate exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d triangle_bcd : ¬collinear b c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

exact ⟨triangle_abc, triangle_abd, triangle_acd, triangle_bcd⟩

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d triangle_bcd : ¬collinear b c d ⊢ isQuadrangle (p ⊔ q) (q ⊔ r) (r ⊔ s) (s ⊔ p)

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply dual_quadrangle_part

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ ¬collinear a b c

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle p q r s

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p ⊢ isQuadrangle p q r s

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply triangle_rotate

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear a b d

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear d a b

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply dual_quadrangle_part

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ ¬collinear d a b

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle s p q r

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle s p q r

case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle r s p q

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle r s p q

case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle q r s p

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle q r s p

case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle p q r s

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c ⊢ isQuadrangle p q r s

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply triangle_rotate

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear a c d

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear d a c

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply triangle_rotate

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear d a c

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear c d a

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply dual_quadrangle_part

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ ¬collinear c d a

case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle r s p q

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle r s p q

case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle q r s p

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle q r s p

case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle p q r s

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

case a.a.a.a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d ⊢ isQuadrangle p q r s

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply dual_quadrangle_part

P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ ¬collinear b c d

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle q r s p

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

apply quadrangle_rotate

case a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle q r s p

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle p q r s

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_quadrangle

[234, 1]

[266, 65]

exact ⟨triangle_pqr, triangle_pqs, triangle_prs, triangle_qrs⟩

case a.a P L : Type p q r s : P inst✝ : ProjectivePlane P triangle_pqr : ¬collinear p q r triangle_pqs : ¬collinear p q s triangle_prs : ¬collinear p r s triangle_qrs : ¬collinear q r s a : line P := p ⊔ q b : line P := q ⊔ r c : line P := r ⊔ s d : line P := s ⊔ p triangle_abc : ¬collinear a b c triangle_abd : ¬collinear a b d triangle_acd : ¬collinear a c d ⊢ isQuadrangle p q r s

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

ProjectivePlane.dual_involution

[281, 1]

[283, 19]

rfl

P L : Type p q r s : P h : ProjectivePlane P ⊢ let h' := inferInstance; h' = h

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

Fano.Fano.quadrangle1236

[383, 1]

[384, 83]

simp[collinear]

P L : Type ⊢ ¬collinear Points.p1 Points.p2 Points.p3

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

Fano.Fano.quadrangle1236

[383, 1]

[384, 83]

simp[collinear]

P L : Type ⊢ ¬collinear Points.p1 Points.p2 Points.p6

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

Fano.Fano.quadrangle1236

[383, 1]

[384, 83]

simp[collinear]

P L : Type ⊢ ¬collinear Points.p1 Points.p3 Points.p6

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

Fano.Fano.quadrangle1236

[383, 1]

[384, 83]

simp[collinear]

P L : Type ⊢ ¬collinear Points.p2 Points.p3 Points.p6

no goals

https://github.com/loewenheim/projective-plane.git

7ade52678ac3df537f38d04de46db9aca752f3ca

ProjectivePlane.lean

Fano.Fano.point_line_uniq

[386, 1]

[387, 9]

decide

P L : Type ⊢ ∀ {p q : Points} {l m : Lines}, p ∈ l → q ∈ l → p ∈ m → q ∈ m → p = q ∨ l = m

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

intro v vars

⊢ ∀ (v : String) (vars : List String), v ∈ vars → String.length v ≤ max_var_name vars

v : String vars : List String ⊢ v ∈ vars → String.length v ≤ max_var_name vars

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

induction vars with | nil => intro hm exact absurd hm (List.not_mem_nil v) | cons x xs ih => intro h rw [List.mem_cons] at h cases h with | inl hvx => unfold max_var_name conv => rhs; rw [← hvx] apply Nat.le_max_left | inr hvxs => unfold max_var_name calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right

v : String vars : List String ⊢ v ∈ vars → String.length v ≤ max_var_name vars

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

intro hm

case nil v : String ⊢ v ∈ [] → String.length v ≤ max_var_name []

case nil v : String hm : v ∈ [] ⊢ String.length v ≤ max_var_name []

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

exact absurd hm (List.not_mem_nil v)

case nil v : String hm : v ∈ [] ⊢ String.length v ≤ max_var_name []

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

intro h

case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs ⊢ v ∈ x :: xs → String.length v ≤ max_var_name (x :: xs)

case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v ∈ x :: xs ⊢ String.length v ≤ max_var_name (x :: xs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

rw [List.mem_cons] at h

case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v ∈ x :: xs ⊢ String.length v ≤ max_var_name (x :: xs)

case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v = x ∨ v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

cases h with | inl hvx => unfold max_var_name conv => rhs; rw [← hvx] apply Nat.le_max_left | inr hvxs => unfold max_var_name calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right

case cons v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs h : v = x ∨ v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

unfold max_var_name

case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ max_var_name (x :: xs)

case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

conv => rhs; rw [← hvx]

case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)

case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length v) (max_var_name xs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

apply Nat.le_max_left

case cons.inl v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvx : v = x ⊢ String.length v ≤ Nat.max (String.length v) (max_var_name xs)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

unfold max_var_name

case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ max_var_name (x :: xs)

case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

calc v.length ≤ max_var_name xs := ih hvxs _ ≤ Nat.max x.length (max_var_name xs) := by apply Nat.le_max_right

case cons.inr v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ String.length v ≤ Nat.max (String.length x) (max_var_name xs)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Fol.lean

max_var_name_mem

[399, 1]

[418, 83]

apply Nat.le_max_right

v x : String xs : List String ih : v ∈ xs → String.length v ≤ max_var_name xs hvxs : v ∈ xs ⊢ max_var_name xs ≤ Nat.max (String.length x) (max_var_name xs)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

intro p inp

⊢ ∀ (p : Char → Bool) (inp : List Char), List.length (lexwhile p inp).snd ≤ List.length inp

p : Char → Bool inp : List Char ⊢ List.length (lexwhile p inp).snd ≤ List.length inp

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

induction inp with | nil => simp [lexwhile] | cons c cs ih => simp [lexwhile] cases p c <;> simp exact Nat.le_succ_of_le ih

p : Char → Bool inp : List Char ⊢ List.length (lexwhile p inp).snd ≤ List.length inp

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

simp [lexwhile]

case nil p : Char → Bool ⊢ List.length (lexwhile p []).snd ≤ List.length []

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

simp [lexwhile]

case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p (c :: cs)).snd ≤ List.length (c :: cs)

case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (if p c = true then (String.append (Char.toString c) (lexwhile p cs).fst, (lexwhile p cs).snd) else ("", c :: cs)).snd ≤ Nat.succ (List.length cs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

cases p c <;> simp

case cons p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (if p c = true then (String.append (Char.toString c) (lexwhile p cs).fst, (lexwhile p cs).snd) else ("", c :: cs)).snd ≤ Nat.succ (List.length cs)

case cons.true p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p cs).snd ≤ Nat.succ (List.length cs)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Parser.lean

lexwhile_monotonic

[35, 1]

[42, 31]

exact Nat.le_succ_of_le ih

case cons.true p : Char → Bool c : Char cs : List Char ih : List.length (lexwhile p cs).snd ≤ List.length cs ⊢ List.length (lexwhile p cs).snd ≤ Nat.succ (List.length cs)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

intro l1 l2

α : Type inst✝¹ : Ord α inst✝ : BEq α ⊢ ∀ (l1 l2 : List α), List.length (merge l1 l2) = List.length l1 + List.length l2

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge l1 l2) = List.length l1 + List.length l2

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

match l1 with | .nil => unfold merge; rw [List.length_nil, Nat.zero_add] | .cons h1 t1 => unfold merge match l2 with | .nil => simp only [List.length_cons, List.length_nil, Nat.add_zero] | .cons h2 t2 => simp only [List.length_cons] split . rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega . rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge l1 l2) = List.length l1 + List.length l2

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

unfold merge

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length (merge [] l2) = List.length [] + List.length l2

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length l2 = List.length [] + List.length l2

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

rw [List.length_nil, Nat.zero_add]

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α ⊢ List.length l2 = List.length [] + List.length l2

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

unfold merge

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (merge (h1 :: t1) l2) = List.length (h1 :: t1) + List.length l2

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match l2 with | [] => h1 :: t1 | l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length l2

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

match l2 with | .nil => simp only [List.length_cons, List.length_nil, Nat.add_zero] | .cons h2 t2 => simp only [List.length_cons] split . rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega . rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match l2 with | [] => h1 :: t1 | l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length l2

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

simp only [List.length_cons, List.length_nil, Nat.add_zero]

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α ⊢ List.length (match [] with | [] => h1 :: t1 | l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length []

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

simp only [List.length_cons]

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (match h2 :: t2 with | [] => h1 :: t1 | l2@h:(h2 :: t2) => let_fun x := (_ : List.length t1 + List.length l2 < List.length (h1 :: t1) + List.length l2); let_fun x := (_ : List.length (h1 :: t1) + List.length t2 < List.length (h1 :: t1) + List.length l2); if isLE (compare h1 h2) = true then h1 :: merge t1 l2 else h2 :: merge (h1 :: t1) t2) = List.length (h1 :: t1) + List.length (h2 :: t2)

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (if isLE (compare h1 h2) = true then h1 :: merge t1 (h2 :: t2) else h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

split

α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α ⊢ List.length (if isLE (compare h1 h2) = true then h1 :: merge t1 (h2 :: t2) else h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2) case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

. rw [List.length_cons, merge_length t1 (h2 :: t2)] simp only [List.length_cons] omega

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2) case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

. rw [List.length_cons, merge_length (h1 :: t1) t2] simp only [List.length_cons] omega

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

rw [List.length_cons, merge_length t1 (h2 :: t2)]

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ List.length (h1 :: merge t1 (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + List.length (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

simp only [List.length_cons]

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + List.length (h2 :: t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + Nat.succ (List.length t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

omega

case inl α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : isLE (compare h1 h2) = true ⊢ Nat.succ (List.length t1 + Nat.succ (List.length t2)) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

rw [List.length_cons, merge_length (h1 :: t1) t2]

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ List.length (h2 :: merge (h1 :: t1) t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (List.length (h1 :: t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

simp only [List.length_cons]

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (List.length (h1 :: t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (Nat.succ (List.length t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Common.lean

Set.merge_length

[105, 1]

[121, 14]

omega

case inr α : Type inst✝¹ : Ord α inst✝ : BEq α l1 l2 : List α h1 : α t1 : List α h2 : α t2 : List α h✝ : ¬isLE (compare h1 h2) = true ⊢ Nat.succ (Nat.succ (List.length t1) + List.length t2) = Nat.succ (List.length t1) + Nat.succ (List.length t2)

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

intro t

α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ ∀ (tr : Trail α), List.length (backtrack tr) ≤ List.length tr

α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α t : Trail α ⊢ List.length (backtrack t) ≤ List.length t

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

induction t with | nil => unfold backtrack; apply Nat.le_refl | cons d ds ih => simp [backtrack] cases d.decision == .Deduced . simp . simp; apply Nat.le_succ_of_le; assumption

α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α t : Trail α ⊢ List.length (backtrack t) ≤ List.length t

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

unfold backtrack

case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length (backtrack []) ≤ List.length []

case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length [] ≤ List.length []

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

apply Nat.le_refl

case nil α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α ⊢ List.length [] ≤ List.length []

no goals

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

simp [backtrack]

case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (backtrack (d :: ds)) ≤ List.length (d :: ds)

case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if (d.decision == LitState.Deduced) = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)

https://github.com/benjaminfjones/reckonlean.git

8768f7342ba226cfc2d7b92e47432f1da66eff25

ReckonLean/Dpll.lean

length_backtrack

[195, 1]

[204, 50]

cases d.decision == .Deduced

case cons α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if (d.decision == LitState.Deduced) = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)

case cons.false α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if false = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds) case cons.true α : Type inst✝³ : BEq α inst✝² : Ord α inst✝¹ : Repr α inst✝ : Hashable α d : Decision α ds : List (Decision α) ih : List.length (backtrack ds) ≤ List.length ds ⊢ List.length (if true = true then backtrack ds else d :: ds) ≤ Nat.succ (List.length ds)