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/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
clear q
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)) →
eval (map (⇑f) s) x = (Finsupp.mapRange.addMonoidHom f) (eval s x)
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)) →
eval (map (⇑f) s) x = (Finsupp.mapRange.addMonoidHom f) (eval s x)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
intro q ih
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)) →
eval (map (⇑f) s) x = (Finsupp.mapRange.addMonoidHom f) (eval s x)
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
by_cases hq : s.valid q
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
case neg
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : ¬s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
swap
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
case neg
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : ¬s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
case neg
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : ¬s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
rw [Stream.eval_invalid, Stream.eval_invalid] <;> simp [hq]
|
case neg
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : ¬s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
rw [s.eval_valid ⟨_, hq⟩, (s.map f).eval_valid ⟨_, hq⟩]
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s q)
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } +
eval (map (⇑f) s) (advance (map (⇑f) s) ↑{ val := q, property := hq }) =
(Finsupp.mapRange.addMonoidHom f)
(eval₀ s { val := q, property := hq } + eval s (advance s ↑{ val := q, property := hq }))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
simp only [map_σ, map_valid, map_add, Finsupp.mapRange.addMonoidHom_apply]
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } +
eval (map (⇑f) s) (advance (map (⇑f) s) ↑{ val := q, property := hq }) =
(Finsupp.mapRange.addMonoidHom f)
(eval₀ s { val := q, property := hq } + eval s (advance s ↑{ val := q, property := hq }))
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } + eval (map (⇑f) s) (advance (map (⇑f) s) q) =
Finsupp.mapRange ⇑f ⋯ (eval₀ s { val := q, property := hq }) + Finsupp.mapRange ⇑f ⋯ (eval s (advance s q))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
congr 1
|
case pos
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } + eval (map (⇑f) s) (advance (map (⇑f) s) q) =
Finsupp.mapRange ⇑f ⋯ (eval₀ s { val := q, property := hq }) + Finsupp.mapRange ⇑f ⋯ (eval s (advance s q))
|
case pos.e_a
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } = Finsupp.mapRange ⇑f ⋯ (eval₀ s { val := q, property := hq })
case pos.e_a
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) (advance (map (⇑f) s) q) = Finsupp.mapRange ⇑f ⋯ (eval s (advance s q))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
rw [Stream.eval₀_map]
|
case pos.e_a
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval₀ (map (⇑f) s) { val := q, property := hq } = Finsupp.mapRange ⇑f ⋯ (eval₀ s { val := q, property := hq })
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
exact ih (s.advance q) (s.next_wf ⟨q, hq⟩)
|
case pos.e_a
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → eval (map (⇑f) s) y = (Finsupp.mapRange.addMonoidHom f) (eval s y)
hq : s.valid q = true
⊢ eval (map (⇑f) s) (advance (map (⇑f) s) q) = Finsupp.mapRange ⇑f ⋯ (eval s (advance s q))
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map_apply
|
[305, 1]
|
[307, 84]
|
rw [Stream.eval_map, Finsupp.mapRange.addMonoidHom_apply, Finsupp.mapRange_apply]
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝³ : Preorder ι
β : Type u_1
inst✝² : AddCommMonoid α
inst✝¹ : AddCommMonoid β
f : α →+ β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ (eval (map (⇑f) s) q) i = f ((eval s q) i)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
have h₁ : (s |> (Stream.map fun x => {x}) |> Stream.map Multiset.sum).eval = s.eval := by
dsimp only [Stream.map_map]
rw [Stream.eval_map_id]
ext; simp
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
have h₂ : (s.evalMultiset q i).sum = (s |> (Stream.map fun x => {x}) |> Stream.map Multiset.sumAddMonoidHom).eval q i := by
rw [Stream.eval_map_apply]
rfl
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
h₂ : Multiset.sum ((evalMultiset s q) i) = (eval (map (⇑Multiset.sumAddMonoidHom) (map (fun x => {x}) s)) q) i
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
rw [Multiset.coe_sumAddMonoidHom] at h₂
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
h₂ : Multiset.sum ((evalMultiset s q) i) = (eval (map (⇑Multiset.sumAddMonoidHom) (map (fun x => {x}) s)) q) i
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
h₂ : Multiset.sum ((evalMultiset s q) i) = (eval (map Multiset.sum (map (fun x => {x}) s)) q) i
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
rw [h₂, h₁]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
h₂ : Multiset.sum ((evalMultiset s q) i) = (eval (map Multiset.sum (map (fun x => {x}) s)) q) i
⊢ Multiset.sum ((evalMultiset s q) i) = (eval s q) i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
dsimp only [Stream.map_map]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ eval (map (Multiset.sum ∘ fun x => {x}) s) = eval s
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
rw [Stream.eval_map_id]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ eval (map (Multiset.sum ∘ fun x => {x}) s) = eval s
|
case hf
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ (Multiset.sum ∘ fun x => {x}) = id
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
ext
|
case hf
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
⊢ (Multiset.sum ∘ fun x => {x}) = id
|
case hf.h
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
x✝ : α
⊢ (Multiset.sum ∘ fun x => {x}) x✝ = id x✝
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
simp
|
case hf.h
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
x✝ : α
⊢ (Multiset.sum ∘ fun x => {x}) x✝ = id x✝
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
rw [Stream.eval_map_apply]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
⊢ Multiset.sum ((evalMultiset s q) i) = (eval (map (⇑Multiset.sumAddMonoidHom) (map (fun x => {x}) s)) q) i
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
⊢ Multiset.sum ((evalMultiset s q) i) = Multiset.sumAddMonoidHom ((eval (map (fun x => {x}) s) q) i)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_sum
|
[309, 1]
|
[319, 14]
|
rfl
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddCommMonoid α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
i : ι
h₁ : eval (map Multiset.sum (map (fun x => {x}) s)) = eval s
⊢ Multiset.sum ((evalMultiset s q) i) = Multiset.sumAddMonoidHom ((eval (map (fun x => {x}) s) q) i)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_zero
|
[321, 1]
|
[322, 29]
|
simp [Stream.evalMultiset]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : 0.σ
i : ι
⊢ (evalMultiset 0 q) i = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_invalid
|
[324, 1]
|
[326, 32]
|
simp [Stream.evalMultiset, h]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
h : ¬s.valid q = true
i : ι
⊢ (evalMultiset s q) i = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_ready
|
[328, 1]
|
[330, 47]
|
simp [Stream.evalMultiset, Stream.eval₀, hr]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
hr : s.ready q = true
⊢ (evalMultiset s ↑q) (s.index q) =
insert (s.value { val := q, property := hr }) ((evalMultiset s (advance s ↑q)) (s.index q))
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
suffices (s.map fun x => ({x} : Multiset α)).eval₀ q i = 0 by
simpa [Stream.evalMultiset]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : ¬s.ready q = true ∨ s.index q ≠ i
⊢ (evalMultiset s ↑q) i = (evalMultiset s (advance s ↑q)) i
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : ¬s.ready q = true ∨ s.index q ≠ i
⊢ (eval₀ (map (fun x => {x}) s) q) i = 0
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
simpa [Stream.evalMultiset]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : ¬s.ready q = true ∨ s.index q ≠ i
this : (eval₀ (map (fun x => {x}) s) q) i = 0
⊢ (evalMultiset s ↑q) i = (evalMultiset s (advance s ↑q)) i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
simp [Stream.eval₀, hr]
|
case inl
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : ¬s.ready q = true
⊢ (eval₀ (map (fun x => {x}) s) q) i = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
simp only [Stream.eval₀]
|
case inr
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
⊢ (eval₀ (map (fun x => {x}) s) q) i = 0
|
case inr
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
⊢ (if h₂ : (map (fun x => {x}) s).ready q = true then
fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h₂ }
else 0)
i =
0
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
split_ifs
|
case inr
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
⊢ (if h₂ : (map (fun x => {x}) s).ready q = true then
fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h₂ }
else 0)
i =
0
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : (map (fun x => {x}) s).ready q = true
⊢ (fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h✝ }) i = 0
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : ¬(map (fun x => {x}) s).ready q = true
⊢ 0 i = 0
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
swap
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : (map (fun x => {x}) s).ready q = true
⊢ (fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h✝ }) i = 0
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : ¬(map (fun x => {x}) s).ready q = true
⊢ 0 i = 0
|
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : ¬(map (fun x => {x}) s).ready q = true
⊢ 0 i = 0
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : (map (fun x => {x}) s).ready q = true
⊢ (fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h✝ }) i = 0
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
simp [hr]
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : (map (fun x => {x}) s).ready q = true
⊢ (fun₀ | (map (fun x => {x}) s).index q => (map (fun x => {x}) s).value { val := q, property := h✝ }) i = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.evalMultiset_not_ready
|
[332, 1]
|
[342, 14]
|
rfl
|
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
i : ι
hr : s.index q ≠ i
h✝ : ¬(map (fun x => {x}) s).ready q = true
⊢ 0 i = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.not_ready_of_toOrder_lt
|
[345, 1]
|
[348, 38]
|
simp only [toOrder, Prod.Lex.lt_iff', lt_true_iff] at h
|
ι✝ : Type
α : Type u_1
a b s✝ : Stream ι✝ α
inst✝¹ : Preorder ι✝
ι : Type
inst✝ : PartialOrder ι
s : Stream ι α
i : ι
q : { q // s.valid q = true }
h : toOrder s q < (i, true)
⊢ ¬s.ready q = true ∨ s.index q ≠ i
|
ι✝ : Type
α : Type u_1
a b s✝ : Stream ι✝ α
inst✝¹ : Preorder ι✝
ι : Type
inst✝ : PartialOrder ι
s : Stream ι α
i : ι
q : { q // s.valid q = true }
h : s.index q < i ∨ s.index q = i ∧ s.ready q = false
⊢ ¬s.ready q = true ∨ s.index q ≠ i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.not_ready_of_toOrder_lt
|
[345, 1]
|
[348, 38]
|
exact h.symm.imp (by simp) ne_of_lt
|
ι✝ : Type
α : Type u_1
a b s✝ : Stream ι✝ α
inst✝¹ : Preorder ι✝
ι : Type
inst✝ : PartialOrder ι
s : Stream ι α
i : ι
q : { q // s.valid q = true }
h : s.index q < i ∨ s.index q = i ∧ s.ready q = false
⊢ ¬s.ready q = true ∨ s.index q ≠ i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.not_ready_of_toOrder_lt
|
[345, 1]
|
[348, 38]
|
simp
|
ι✝ : Type
α : Type u_1
a b s✝ : Stream ι✝ α
inst✝¹ : Preorder ι✝
ι : Type
inst✝ : PartialOrder ι
s : Stream ι α
i : ι
q : { q // s.valid q = true }
h : s.index q < i ∨ s.index q = i ∧ s.ready q = false
⊢ s.index q = i ∧ s.ready q = false → ¬s.ready q = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support
|
[351, 1]
|
[358, 9]
|
rw [Stream.eval₀]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
⊢ (eval₀ s x).support ⊆ {s.index x}
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
⊢ (if h₂ : s.ready x = true then fun₀ | s.index x => s.value { val := x, property := h₂ } else 0).support ⊆ {s.index x}
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support
|
[351, 1]
|
[358, 9]
|
split_ifs
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
⊢ (if h₂ : s.ready x = true then fun₀ | s.index x => s.value { val := x, property := h₂ } else 0).support ⊆ {s.index x}
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h✝ : s.ready x = true
⊢ (fun₀ | s.index x => s.value { val := x, property := h✝ }).support ⊆ {s.index x}
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h✝ : ¬s.ready x = true
⊢ 0.support ⊆ {s.index x}
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support
|
[351, 1]
|
[358, 9]
|
exact Finsupp.support_single_subset
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h✝ : s.ready x = true
⊢ (fun₀ | s.index x => s.value { val := x, property := h✝ }).support ⊆ {s.index x}
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support
|
[351, 1]
|
[358, 9]
|
simp
|
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h✝ : ¬s.ready x = true
⊢ 0.support ⊆ {s.index x}
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support'
|
[361, 1]
|
[369, 15]
|
obtain rfl := Finset.eq_of_mem_singleton (s.eval₀_support x (Finsupp.mem_support_iff.mpr h₂))
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
i : ι
h₂ : (eval₀ s x) i ≠ 0
⊢ toOrder s x = (i, true)
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h₂ : (eval₀ s x) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support'
|
[361, 1]
|
[369, 15]
|
rw [Stream.eval₀] at h₂
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h₂ : (eval₀ s x) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h₂ : (if h₂ : s.ready x = true then fun₀ | s.index x => s.value { val := x, property := h₂ } else 0) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support'
|
[361, 1]
|
[369, 15]
|
split_ifs at h₂ with hr
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
h₂ : (if h₂ : s.ready x = true then fun₀ | s.index x => s.value { val := x, property := h₂ } else 0) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
hr : s.ready x = true
h₂ : (fun₀ | s.index x => s.value { val := x, property := hr }) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
hr : ¬s.ready x = true
h₂ : 0 (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support'
|
[361, 1]
|
[369, 15]
|
simp [Stream.toOrder, hr]
|
case pos
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
hr : s.ready x = true
h₂ : (fun₀ | s.index x => s.value { val := x, property := hr }) (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_support'
|
[361, 1]
|
[369, 15]
|
simp at h₂
|
case neg
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : Zero α
s : Stream ι α
inst✝ : IsBounded s
x : { q // s.valid q = true }
hr : ¬s.ready x = true
h₂ : 0 (s.index x) ≠ 0
⊢ toOrder s x = (s.index x, true)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.fold_wf_spec
|
[391, 1]
|
[397, 6]
|
rw [Stream.fold_wf, fold_wf.go]
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
acc : β
⊢ fold_wf f s (↑q) acc =
fold_wf f s (advance s ↑q)
(if hr : s.ready q = true then f acc (s.index q) (s.value { val := q, property := hr }) else acc)
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
acc : β
⊢ (if hv : s.valid ↑q = true then
let i := s.index { val := ↑q, property := hv };
let hr := s.ready { val := ↑q, property := hv };
let q' := next s { val := ↑q, property := hv } i hr;
let acc' :=
if hr : hr = true then f acc i (s.value { val := { val := ↑q, property := hv }, property := hr }) else acc;
fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯ acc' q'
else acc) =
fold_wf f s (advance s ↑q)
(if hr : s.ready q = true then f acc (s.index q) (s.value { val := q, property := hr }) else acc)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.fold_wf_spec
|
[391, 1]
|
[397, 6]
|
simp only [q.prop, Subtype.coe_eta, dite_true, advance_val]
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
acc : β
⊢ (if hv : s.valid ↑q = true then
let i := s.index { val := ↑q, property := hv };
let hr := s.ready { val := ↑q, property := hv };
let q' := next s { val := ↑q, property := hv } i hr;
let acc' :=
if hr : hr = true then f acc i (s.value { val := { val := ↑q, property := hv }, property := hr }) else acc;
fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯ acc' q'
else acc) =
fold_wf f s (advance s ↑q)
(if hr : s.ready q = true then f acc (s.index q) (s.value { val := q, property := hr }) else acc)
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
acc : β
⊢ fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯
(if h : s.ready q = true then f acc (s.index q) (s.value { val := q, property := ⋯ }) else acc)
(next s q (s.index q) (s.ready q)) =
fold_wf f s (s.seek q (toOrder s q))
(if hr : s.ready q = true then f acc (s.index q) (s.value { val := q, property := hr }) else acc)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.fold_wf_spec
|
[391, 1]
|
[397, 6]
|
rfl
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
acc : β
⊢ fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯
(if h : s.ready q = true then f acc (s.index q) (s.value { val := q, property := ⋯ }) else acc)
(next s q (s.index q) (s.ready q)) =
fold_wf f s (s.seek q (toOrder s q))
(if hr : s.ready q = true then f acc (s.index q) (s.value { val := q, property := hr }) else acc)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.fold_wf_invalid
|
[405, 1]
|
[408, 11]
|
rw [Stream.fold_wf, fold_wf.go]
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
acc : β
h : ¬s.valid q = true
⊢ fold_wf f s q acc = acc
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
acc : β
h : ¬s.valid q = true
⊢ (if hv : s.valid q = true then
let i := s.index { val := q, property := hv };
let hr := s.ready { val := q, property := hv };
let q' := next s { val := q, property := hv } i hr;
let acc' :=
if hr : hr = true then f acc i (s.value { val := { val := q, property := hv }, property := hr }) else acc;
fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯ acc' q'
else acc) =
acc
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.fold_wf_invalid
|
[405, 1]
|
[408, 11]
|
simp [h]
|
ι : Type
α : Type u_2
a b s✝ : Stream ι α
inst✝¹ : Preorder ι
β : Sort u_1
f : β → ι → α → β
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
acc : β
h : ¬s.valid q = true
⊢ (if hv : s.valid q = true then
let i := s.index { val := q, property := hv };
let hr := s.ready { val := q, property := hv };
let q' := next s { val := q, property := hv } i hr;
let acc' :=
if hr : hr = true then f acc i (s.value { val := { val := q, property := hv }, property := hr }) else acc;
fold_wf.go s f s.valid (fun q h => s.ready { val := q, property := h })
(fun q h => s.index { val := q, property := h })
(fun q v r => s.value { val := { val := q, property := v }, property := r }) (next s) ⋯ acc' q'
else acc) =
acc
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_isMonotonic
|
[422, 9]
|
[423, 52]
|
rfl
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
β : Type u_2
s : Stream ι α
f : α → β
⊢ IsMonotonic (map f s) ↔ IsMonotonic s
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_isStrictMono
|
[430, 9]
|
[431, 54]
|
rfl
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
β : Type u_2
s : Stream ι α
f : α → β
⊢ IsStrictMono (map f s) ↔ IsStrictMono s
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
constructor
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
⊢ IsMonotonic s ↔
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
|
case mp
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
⊢ IsMonotonic s →
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
case mpr
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
⊢ (∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }) →
IsMonotonic s
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
intro h q i hq
|
case mp
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
⊢ IsMonotonic s →
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
|
case mp
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : { x // s.valid x = true }
i : Lex (ι × Bool)
hq : s.valid (s.seek q i) = true
⊢ s.index q ≤ s.index { val := s.seek q i, property := hq }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
simpa [index'_val' _ hq] using h q i
|
case mp
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : { x // s.valid x = true }
i : Lex (ι × Bool)
hq : s.valid (s.seek q i) = true
⊢ s.index q ≤ s.index { val := s.seek q i, property := hq }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
intro h q i
|
case mpr
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
⊢ (∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }) →
IsMonotonic s
|
case mpr
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
by_cases hq' : s.valid (s.seek q i)
|
case mpr
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = true
⊢ index' s ↑q ≤ index' s (s.seek q i)
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : ¬s.valid (s.seek q i) = true
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
simpa [index'_val' _ hq'] using h q i hq'
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = true
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
rw [Bool.not_eq_true] at hq'
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : ¬s.valid (s.seek q i) = true
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = false
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
rw [Stream.index'_invalid hq']
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = false
⊢ index' s ↑q ≤ index' s (s.seek q i)
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = false
⊢ index' s ↑q ≤ ⊤
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.isMonotonic_iff
|
[433, 1]
|
[443, 19]
|
exact le_top
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h :
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)) (hq : s.valid (s.seek q i) = true),
s.index q ≤ s.index { val := s.seek q i, property := hq }
q : { q // s.valid q = true }
i : Lex (ι × Bool)
hq' : s.valid (s.seek q i) = false
⊢ index' s ↑q ≤ ⊤
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_index_advance
|
[445, 1]
|
[450, 12]
|
by_cases H : s.valid q
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
⊢ index' s q ≤ index' s (advance s q)
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : ¬s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_index_advance
|
[445, 1]
|
[450, 12]
|
swap
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : ¬s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : ¬s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_index_advance
|
[445, 1]
|
[450, 12]
|
simp [H]
|
case neg
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : ¬s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_index_advance
|
[445, 1]
|
[450, 12]
|
simp only [Stream.advance, H, dif_pos]
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (advance s q)
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (s.seek { val := q, property := ⋯ } (toOrder s { val := q, property := ⋯ }))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_index_advance
|
[445, 1]
|
[450, 12]
|
apply h
|
case pos
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
h : IsMonotonic s
q : s.σ
H : s.valid q = true
⊢ index' s q ≤ index' s (s.seek { val := q, property := ⋯ } (toOrder s { val := q, property := ⋯ }))
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
simp only [← Finsupp.mem_support_iff]
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
⊢ ∀ (i : ι), (eval s q) i ≠ 0 → index' s q ≤ ↑i
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
⊢ ∀ i ∈ (eval s q).support, index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
apply s.wf.induction q
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
⊢ ∀ i ∈ (eval s q).support, index' s q ≤ ↑i
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i) → ∀ i ∈ (eval s x).support, index' s x ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
clear q
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i) → ∀ i ∈ (eval s x).support, index' s x ≤ ↑i
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i) → ∀ i ∈ (eval s x).support, index' s x ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
intro q ih i hi
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
⊢ ∀ (x : s.σ),
(∀ (y : s.σ), WfRel s y x → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i) → ∀ i ∈ (eval s x).support, index' s x ≤ ↑i
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
⊢ index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
by_cases H : s.valid q
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
⊢ index' s q ≤ ↑i
|
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : s.valid q = true
⊢ index' s q ≤ ↑i
case neg
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : ¬s.valid q = true
⊢ index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
swap
|
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : s.valid q = true
⊢ index' s q ≤ ↑i
case neg
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : ¬s.valid q = true
⊢ index' s q ≤ ↑i
|
case neg
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : ¬s.valid q = true
⊢ index' s q ≤ ↑i
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : s.valid q = true
⊢ index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
simp [H] at hi
|
case neg
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : ¬s.valid q = true
⊢ index' s q ≤ ↑i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
rw [s.eval_valid ⟨_, H⟩] at hi
|
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
hi : i ∈ (eval s q).support
H : s.valid q = true
⊢ index' s q ≤ ↑i
|
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
⊢ index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
rcases Finset.mem_union.mp (Finsupp.support_add hi) with hi | hi
|
case pos
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
⊢ index' s q ≤ ↑i
|
case pos.inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval₀ s { val := q, property := H }).support
⊢ index' s q ≤ ↑i
case pos.inr
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval s (advance s ↑{ val := q, property := H })).support
⊢ index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
rw [Finset.mem_singleton.mp (s.eval₀_support ⟨_, H⟩ hi)]
|
case pos.inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval₀ s { val := q, property := H }).support
⊢ index' s q ≤ ↑i
|
case pos.inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval₀ s { val := q, property := H }).support
⊢ index' s q ≤ ↑(s.index { val := q, property := H })
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
exact le_of_eq (Stream.index'_val' _ _)
|
case pos.inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval₀ s { val := q, property := H }).support
⊢ index' s q ≤ ↑(s.index { val := q, property := H })
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.index_le_of_mem_support
|
[452, 1]
|
[464, 91]
|
exact (hs.index_le_index_advance q).trans (ih (s.advance q) (s.next_wf ⟨q, H⟩) i hi)
|
case pos.inr
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
ih : ∀ (y : s.σ), WfRel s y q → ∀ i ∈ (eval s y).support, index' s y ≤ ↑i
i : ι
H : s.valid q = true
hi✝ : i ∈ (eval₀ s { val := q, property := H } + eval s (advance s ↑{ val := q, property := H })).support
hi : i ∈ (eval s (advance s ↑{ val := q, property := H })).support
⊢ index' s q ≤ ↑i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.eq_zero_of_lt_index
|
[470, 1]
|
[473, 37]
|
contrapose!
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ ↑i < index' s q → (eval s q) i = 0
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ (eval s q) i ≠ 0 → index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.eq_zero_of_lt_index
|
[470, 1]
|
[473, 37]
|
exact hs.index_le_of_mem_support i
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ (eval s q) i ≠ 0 → index' s q ≤ ↑i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.eq_empty_of_lt_index
|
[475, 1]
|
[478, 43]
|
contrapose!
|
ι : Type
inst✝¹ : LinearOrder ι
α : Type u_1
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ ↑i < index' s q → (evalMultiset s q) i = 0
|
ι : Type
inst✝¹ : LinearOrder ι
α : Type u_1
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ (evalMultiset s q) i ≠ 0 → index' s q ≤ ↑i
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsMonotonic.eq_empty_of_lt_index
|
[475, 1]
|
[478, 43]
|
exact hs.index_le_of_nonempty_multiset i
|
ι : Type
inst✝¹ : LinearOrder ι
α : Type u_1
s : Stream ι α
inst✝ : IsBounded s
hs : IsMonotonic s
q : s.σ
i : ι
⊢ (evalMultiset s q) i ≠ 0 → index' s q ≤ ↑i
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.lt'
|
[484, 1]
|
[486, 28]
|
simpa using hs.lt H hr
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
H : toOrder s q ≤ i
hr : s.ready q = true
⊢ ↑(s.index q) < index' s (s.seek q i)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.advance_ne
|
[488, 1]
|
[491, 27]
|
rw [Stream.advance_val]
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
hr : s.ready q = true
⊢ index' s ↑q ≠ index' s (advance s ↑q)
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
hr : s.ready q = true
⊢ index' s ↑q ≠ index' s (s.seek q (toOrder s q))
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.advance_ne
|
[488, 1]
|
[491, 27]
|
exact hs.2 q _ rfl.le hr
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
hr : s.ready q = true
⊢ index' s ↑q ≠ index' s (s.seek q (toOrder s q))
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.spec
|
[493, 1]
|
[499, 31]
|
simpa using hs.1 q i
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ (toOrder' s ↑q).1 ≤ (index' s (s.seek q i), false).1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.spec
|
[493, 1]
|
[499, 31]
|
simp
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ (toOrder' s ↑q).1 = (index' s (s.seek q i), false).1 → (toOrder' s ↑q).2 ≤ (index' s (s.seek q i), false).2
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ ↑(s.index q) = index' s (s.seek q i) → s.ready q = false
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.spec
|
[493, 1]
|
[499, 31]
|
contrapose
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ ↑(s.index q) = index' s (s.seek q i) → s.ready q = false
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ ¬s.ready q = false → ¬↑(s.index q) = index' s (s.seek q i)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.spec
|
[493, 1]
|
[499, 31]
|
simpa using hs.2 q i hi
|
ι : Type
inst✝ : LinearOrder ι
α : Type u_1
s : Stream ι α
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
⊢ ¬s.ready q = false → ¬↑(s.index q) = index' s (s.seek q i)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.index_le_of_mem_support
|
[501, 1]
|
[508, 53]
|
rw [← Stream.coeLex_toOrder]
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
hj : (eval s (s.seek q i)) j ≠ 0
⊢ coeLex (toOrder s q) ≤ coeLex (j, false)
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
hj : (eval s (s.seek q i)) j ≠ 0
⊢ toOrder' s ↑q ≤ coeLex (j, false)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.index_le_of_mem_support
|
[501, 1]
|
[508, 53]
|
refine (hs.spec q hi).trans ?_
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
hj : (eval s (s.seek q i)) j ≠ 0
⊢ toOrder' s ↑q ≤ coeLex (j, false)
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
hj : (eval s (s.seek q i)) j ≠ 0
⊢ (index' s (s.seek q i), false) ≤ coeLex (j, false)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.index_le_of_mem_support
|
[501, 1]
|
[508, 53]
|
simpa using hs.1.index_le_of_mem_support j hj
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
hj : (eval s (s.seek q i)) j ≠ 0
⊢ (index' s (s.seek q i), false) ≤ coeLex (j, false)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eq_zero_of_lt_index
|
[510, 1]
|
[514, 48]
|
contrapose
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
⊢ (j, false) < toOrder s q → (eval s (s.seek q i)) j = 0
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
⊢ ¬(eval s (s.seek q i)) j = 0 → ¬(j, false) < toOrder s q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eq_zero_of_lt_index
|
[510, 1]
|
[514, 48]
|
simpa using hs.index_le_of_mem_support q hi j
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
hi : toOrder s q ≤ i
j : ι
⊢ ¬(eval s (s.seek q i)) j = 0 → ¬(j, false) < toOrder s q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.fst_lt_of_lt_of_lt
|
[516, 1]
|
[523, 36]
|
simp
|
ι : Type ?u.114137
inst✝¹ : LinearOrder ι
α : Type u_1
inst✝ : Preorder α
x y : Lex (α × Bool)
z : α
h₁ : x < y
h₂ : y < (z, false)
⊢ (z, false).2 ≤ x.2
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.fst_lt_of_lt_of_lt
|
[516, 1]
|
[523, 36]
|
simpa using h₂
|
ι : Type ?u.114137
inst✝¹ : LinearOrder ι
α : Type u_1
inst✝ : Preorder α
x : Lex (α × Bool)
y z : α
h₁ : x < (y, true)
h₂ : (y, true) < (z, true)
⊢ y < (z, true).1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.fst_lt_of_lt_of_lt
|
[516, 1]
|
[523, 36]
|
simp
|
ι : Type ?u.114137
inst✝¹ : LinearOrder ι
α : Type u_1
inst✝ : Preorder α
x : Lex (α × Bool)
y z : α
h₁ : x < (y, false)
h₂ : (y, false) < (z, true)
⊢ (y, false).2 ≤ x.2
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eval_seek_eq_zero
|
[525, 1]
|
[533, 41]
|
rcases eq_or_lt_of_le h₂ with h₂ | h₂
|
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂ : i ≤ toOrder s q
⊢ (eval s (s.seek q i)) j = 0
|
case inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i = toOrder s q
⊢ (eval s (s.seek q i)) j = 0
case inr
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i < toOrder s q
⊢ (eval s (s.seek q i)) j = 0
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eval_seek_eq_zero
|
[525, 1]
|
[533, 41]
|
refine hs.eq_zero_of_lt_index _ h₂.symm.le _ ?_
|
case inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i = toOrder s q
⊢ (eval s (s.seek q i)) j = 0
|
case inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i = toOrder s q
⊢ (j, false) < toOrder s q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eval_seek_eq_zero
|
[525, 1]
|
[533, 41]
|
rwa [← h₂]
|
case inl
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i = toOrder s q
⊢ (j, false) < toOrder s q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.IsStrictMono.eval_seek_eq_zero
|
[525, 1]
|
[533, 41]
|
apply hs.1.eq_zero_of_lt_index
|
case inr
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i < toOrder s q
⊢ (eval s (s.seek q i)) j = 0
|
case inr.a
ι : Type
inst✝² : LinearOrder ι
α : Type u_1
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
hs : IsStrictMono s
q : { q // s.valid q = true }
i : StreamOrder ι
j : ι
h₁ : (j, false) < i
h₂✝ : i ≤ toOrder s q
h₂ : i < toOrder s q
⊢ ↑j < index' s (s.seek q i)
|
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