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/StreamMul.lean
|
Etch.Verification.Stream.mul_spec
|
[156, 1]
|
[167, 9]
|
rw [Stream.eval_valid _ ⟨_, hv⟩, ih _ ((a.mul b).next_wf ⟨q, hv⟩), next_eval_mul_eq _ _ ⟨_, hv⟩,
mul_eval₀_spec _ _ a.strictMono b.strictMono ⟨_, hv⟩]
|
case pos
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : (mul a b).σ
ih : ∀ (y : (mul a b).σ), WfRel (mul a b) y q → eval (mul a b) y = eval a y.1 * eval b y.2
hv : (mul a b).valid q = true
⊢ eval (mul a b) q = eval a q.1 * eval b q.2
|
case pos
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : (mul a b).σ
ih : ∀ (y : (mul a b).σ), WfRel (mul a b) y q → eval (mul a b) y = eval a y.1 * eval b y.2
hv : (mul a b).valid q = true
⊢ Finsupp.filter (fun i => (i, false) < toOrder (mul a b) { val := q, property := hv })
(eval a ↑(mul.valid.fst { val := q, property := hv }) * eval b ↑(mul.valid.snd { val := q, property := hv })) +
Finsupp.filter (fun i => toOrder (mul a b) { val := q, property := hv } ≤ (i, false))
(eval a ↑(mul.valid.fst { val := q, property := hv }) * eval b ↑(mul.valid.snd { val := q, property := hv })) =
eval a q.1 * eval b q.2
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamMul.lean
|
Etch.Verification.Stream.mul_spec
|
[156, 1]
|
[167, 9]
|
convert Finsupp.filter_pos_add_filter_neg (α := ι) (M := α) ..
|
case pos
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : (mul a b).σ
ih : ∀ (y : (mul a b).σ), WfRel (mul a b) y q → eval (mul a b) y = eval a y.1 * eval b y.2
hv : (mul a b).valid q = true
⊢ Finsupp.filter (fun i => (i, false) < toOrder (mul a b) { val := q, property := hv })
(eval a ↑(mul.valid.fst { val := q, property := hv }) * eval b ↑(mul.valid.snd { val := q, property := hv })) +
Finsupp.filter (fun i => toOrder (mul a b) { val := q, property := hv } ≤ (i, false))
(eval a ↑(mul.valid.fst { val := q, property := hv }) * eval b ↑(mul.valid.snd { val := q, property := hv })) =
eval a q.1 * eval b q.2
|
case h.e'_2.h.e'_6.h.e'_4.h.a
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : (mul a b).σ
ih : ∀ (y : (mul a b).σ), WfRel (mul a b) y q → eval (mul a b) y = eval a y.1 * eval b y.2
hv : (mul a b).valid q = true
x✝ : ι
⊢ toOrder (mul a b) { val := q, property := hv } ≤ (x✝, false) ↔
¬(x✝, false) < toOrder (mul a b) { val := q, property := hv }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamMul.lean
|
Etch.Verification.Stream.mul_spec
|
[156, 1]
|
[167, 9]
|
simp
|
case h.e'_2.h.e'_6.h.e'_4.h.a
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : (mul a b).σ
ih : ∀ (y : (mul a b).σ), WfRel (mul a b) y q → eval (mul a b) y = eval a y.1 * eval b y.2
hv : (mul a b).valid q = true
x✝ : ι
⊢ toOrder (mul a b) { val := q, property := hv } ≤ (x✝, false) ↔
¬(x✝, false) < toOrder (mul a b) { val := q, property := hv }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamMul.lean
|
Etch.Verification.Stream.mul_seek_spec
|
[169, 1]
|
[173, 58]
|
simp only [Finsupp.mul_apply, mul_spec]
|
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : { q // (mul a b).valid q = true }
i : Lex (ι × Bool)
j : ι
h : i ≤ (j, false)
⊢ (eval (mul a b) ((mul a b).seek q i)) j = (eval (mul a b) ↑q) j
|
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : { q // (mul a b).valid q = true }
i : Lex (ι × Bool)
j : ι
h : i ≤ (j, false)
⊢ (eval a ((mul a b).seek q i).1) j * (eval b ((mul a b).seek q i).2) j = (eval a (↑q).1) j * (eval b (↑q).2) j
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamMul.lean
|
Etch.Verification.Stream.mul_seek_spec
|
[169, 1]
|
[173, 58]
|
congr 1 <;> dsimp <;> rw [IsLawful.seek_spec] <;> aesop
|
ι : Type
inst✝³ : LinearOrder ι
α : Type u
inst✝² : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst✝¹ : IsStrictLawful a
inst✝ : IsStrictLawful b
q : { q // (mul a b).valid q = true }
i : Lex (ι × Bool)
j : ι
h : i ≤ (j, false)
⊢ (eval a ((mul a b).seek q i).1) j * (eval b ((mul a b).seek q i).2) j = (eval a (↑q).1) j * (eval b (↑q).2) j
|
ι : Type
inst : LinearOrder ι
α : Type u
inst_1 : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst_2 : IsStrictLawful a
inst_3 : IsStrictLawful b
i : Lex (ι × Bool)
j : ι
h : i ≤ (j, false)
val : (mul a b).σ
property : (mul a b).valid val = true
⊢ (eval a (a.seek (mul.valid.fst { val := val, property := property }) i)) j = (eval a val.1) j
ι : Type
inst : LinearOrder ι
α : Type u
inst_1 : NonUnitalNonAssocSemiring α
a b : Stream ι α
inst_2 : IsStrictLawful a
inst_3 : IsStrictLawful b
i : Lex (ι × Bool)
j : ι
h : i ≤ (j, false)
val : (mul a b).σ
property : (mul a b).valid val = true
⊢ (eval b (b.seek (mul.valid.snd { val := val, property := property }) i)) j = (eval b val.2) j
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.min?_mem
|
[16, 1]
|
[19, 54]
|
rw [min?_eq_toList_head?] at h
|
α : Type u_1
a : α
t : RBNode α
h : RBNode.min? t = some a
⊢ a ∈ t
|
α : Type u_1
a : α
t : RBNode α
h : List.head? (toList t) = some a
⊢ a ∈ t
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.min?_mem
|
[16, 1]
|
[19, 54]
|
rw [← mem_toList]
|
α : Type u_1
a : α
t : RBNode α
h : List.head? (toList t) = some a
⊢ a ∈ t
|
α : Type u_1
a : α
t : RBNode α
h : List.head? (toList t) = some a
⊢ a ∈ toList t
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.min?_mem
|
[16, 1]
|
[19, 54]
|
revert h
|
α : Type u_1
a : α
t : RBNode α
h : List.head? (toList t) = some a
⊢ a ∈ toList t
|
α : Type u_1
a : α
t : RBNode α
⊢ List.head? (toList t) = some a → a ∈ toList t
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.min?_mem
|
[16, 1]
|
[19, 54]
|
cases toList t <;> rintro ⟨⟩
|
α : Type u_1
a : α
t : RBNode α
⊢ List.head? (toList t) = some a → a ∈ toList t
|
case cons.refl
α : Type u_1
a : α
t : RBNode α
tail✝ : List α
⊢ a ∈ a :: tail✝
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.min?_mem
|
[16, 1]
|
[19, 54]
|
constructor
|
case cons.refl
α : Type u_1
a : α
t : RBNode α
tail✝ : List α
⊢ a ∈ a :: tail✝
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
rw [min?_eq_toList_head?] at h
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : RBNode.min? t = some a
x : α
hx : x ∈ t
⊢ cmp a x ≠ Ordering.gt
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ t
⊢ cmp a x ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
rw [← mem_toList] at hx
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ t
⊢ cmp a x ≠ Ordering.gt
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ toList t
⊢ cmp a x ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
have := ht.toList_sorted
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ toList t
⊢ cmp a x ≠ Ordering.gt
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ toList t
this : List.Pairwise (cmpLT cmp) (toList t)
⊢ cmp a x ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
revert h hx this
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : List.head? (toList t) = some a
x : α
hx : x ∈ toList t
this : List.Pairwise (cmpLT cmp) (toList t)
⊢ cmp a x ≠ Ordering.gt
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
⊢ List.head? (toList t) = some a → x ∈ toList t → List.Pairwise (cmpLT cmp) (toList t) → cmp a x ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
cases toList t <;> rintro ⟨⟩ (_ | ⟨_, hx⟩) (_ | ⟨h1,h2⟩)
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
⊢ List.head? (toList t) = some a → x ∈ toList t → List.Pairwise (cmpLT cmp) (toList t) → cmp a x ≠ Ordering.gt
|
case cons.refl.head.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
tail✝ : List α
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ cmp a a ≠ Ordering.gt
case cons.refl.tail.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
tail✝ : List α
hx : List.Mem x tail✝
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ cmp a x ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
rw [OrientedCmp.cmp_refl (cmp := cmp)]
|
case cons.refl.head.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
tail✝ : List α
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ cmp a a ≠ Ordering.gt
|
case cons.refl.head.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
tail✝ : List α
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ Ordering.eq ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
decide
|
case cons.refl.head.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
tail✝ : List α
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ Ordering.eq ≠ Ordering.gt
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
rw [(h1 _ hx).1]
|
case cons.refl.tail.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
tail✝ : List α
hx : List.Mem x tail✝
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ cmp a x ≠ Ordering.gt
|
case cons.refl.tail.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
tail✝ : List α
hx : List.Mem x tail✝
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ Ordering.lt ≠ Ordering.gt
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.min?_le
|
[21, 1]
|
[28, 29]
|
decide
|
case cons.refl.tail.cons
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
x : α
tail✝ : List α
hx : List.Mem x tail✝
h2 : List.Pairwise (cmpLT cmp) tail✝
h1 : ∀ (a' : α), a' ∈ tail✝ → cmpLT cmp a a'
⊢ Ordering.lt ≠ Ordering.gt
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.max?_mem
|
[30, 1]
|
[31, 50]
|
simpa using min?_mem ((min?_reverse _).trans h)
|
α : Type u_1
a : α
t : RBNode α
h : RBNode.max? t = some a
⊢ a ∈ t
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBNode.Ordered.le_max?
|
[33, 1]
|
[35, 70]
|
simpa using hx
|
α : Type u_1
cmp : α → α → Ordering
a : α
t : RBNode α
inst✝ : TransCmp cmp
ht : Ordered cmp t
h : RBNode.max? t = some a
x : α
hx : x ∈ t
⊢ x ∈ reverse t
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.isEmpty_iff_toList_eq_nil
|
[48, 1]
|
[49, 83]
|
obtain ⟨⟨⟩, _⟩ := t <;> simp [toList, isEmpty]
|
α : Type u_1
cmp : α → α → Ordering
t : RBSet α cmp
⊢ isEmpty t = true ↔ toList t = []
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_some
|
[60, 1]
|
[62, 53]
|
simp [mem_toList]
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
y : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
⊢ y ∈ t.val ∧ cut y = Ordering.eq ↔ y ∈ toList t ∧ cut y = Ordering.eq
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
refine Option.ext fun u =>
findP?_some.trans <| .trans (and_congr_left fun h' => ?_) findP?_some.symm
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
⊢ findP? (insert t v) cut = findP? t cut
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ u ∈ toList (insert t v) ↔ u ∈ toList t
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
rw [mem_toList_insert, or_iff_left, and_iff_left]
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ u ∈ toList (insert t v) ↔ u ∈ toList t
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ find? t v ≠ some u
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ ¬u = v
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
exact mt (fun h => by rwa [IsCut.congr (cut := cut) (find?_some_eq_eq h)]) h
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ find? t v ≠ some u
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
rwa [IsCut.congr (cut := cut) (find?_some_eq_eq h)]
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h✝ : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
h : find? t v = some u
⊢ cut v = Ordering.eq
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
rintro rfl
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
v : α
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
h : cut v ≠ Ordering.eq
u : α
h' : cut u = Ordering.eq
⊢ ¬u = v
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
u : α
h' : cut u = Ordering.eq
h : cut u ≠ Ordering.eq
⊢ False
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert_of_ne
|
[71, 1]
|
[77, 30]
|
contradiction
|
α : Type u_1
cmp : α → α → Ordering
cut : α → Ordering
inst✝¹ : TransCmp cmp
inst✝ : IsStrictCut cmp cut
t : RBSet α cmp
u : α
h' : cut u = Ordering.eq
h : cut u ≠ Ordering.eq
⊢ False
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.findP?_insert
|
[79, 1]
|
[81, 79]
|
split <;> [exact findP?_insert_of_eq t ‹_›; exact findP?_insert_of_ne t ‹_›]
|
α : Type u_1
cmp : α → α → Ordering
inst✝¹ : TransCmp cmp
t : RBSet α cmp
v : α
cut : α → Ordering
inst✝ : IsStrictCut cmp cut
⊢ findP? (insert t v) cut = if cut v = Ordering.eq then some v else findP? t cut
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.isEmpty_iff_eq_empty
|
[83, 1]
|
[88, 9]
|
obtain ⟨⟨⟩, _⟩ := t <;>
simp [isEmpty]
|
α : Type u_1
cmp : α → α → Ordering
t : RBSet α cmp
⊢ isEmpty t = true ↔ t = ∅
|
case mk.nil
α : Type u_1
cmp : α → α → Ordering
property✝ : RBNode.WF cmp RBNode.nil
⊢ { val := RBNode.nil, property := property✝ } = ∅
case mk.node
α : Type u_1
cmp : α → α → Ordering
c✝ : RBColor
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
property✝ : RBNode.WF cmp (RBNode.node c✝ l✝ v✝ r✝)
⊢ ¬{ val := RBNode.node c✝ l✝ v✝ r✝, property := property✝ } = ∅
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.isEmpty_iff_eq_empty
|
[83, 1]
|
[88, 9]
|
rfl
|
case mk.nil
α : Type u_1
cmp : α → α → Ordering
property✝ : RBNode.WF cmp RBNode.nil
⊢ { val := RBNode.nil, property := property✝ } = ∅
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.isEmpty_iff_eq_empty
|
[83, 1]
|
[88, 9]
|
change _ ≠ Subtype.mk _ _
|
case mk.node
α : Type u_1
cmp : α → α → Ordering
c✝ : RBColor
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
property✝ : RBNode.WF cmp (RBNode.node c✝ l✝ v✝ r✝)
⊢ ¬{ val := RBNode.node c✝ l✝ v✝ r✝, property := property✝ } = ∅
|
case mk.node
α : Type u_1
cmp : α → α → Ordering
c✝ : RBColor
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
property✝ : RBNode.WF cmp (RBNode.node c✝ l✝ v✝ r✝)
⊢ { val := RBNode.node c✝ l✝ v✝ r✝, property := property✝ } ≠ { val := RBNode.nil, property := ⋯ }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBSet.isEmpty_iff_eq_empty
|
[83, 1]
|
[88, 9]
|
simp
|
case mk.node
α : Type u_1
cmp : α → α → Ordering
c✝ : RBColor
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
property✝ : RBNode.WF cmp (RBNode.node c✝ l✝ v✝ r✝)
⊢ { val := RBNode.node c✝ l✝ v✝ r✝, property := property✝ } ≠ { val := RBNode.nil, property := ⋯ }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some_mem_toList
|
[141, 1]
|
[144, 69]
|
obtain ⟨⟨y, v⟩, h', rfl⟩ := Option.map_eq_some'.1 h
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
x : α
v : β
t : RBMap α β cmp
h : find? t x = some v
⊢ ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
|
case intro.mk.intro
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
x : α
t : RBMap α β cmp
y : α
v : β
h' : findEntry? t x = some (y, v)
h : find? t x = some (y, v).snd
⊢ ∃ y_1, (y_1, (y, v).snd) ∈ toList t ∧ cmp x y_1 = Ordering.eq
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some_mem_toList
|
[141, 1]
|
[144, 69]
|
exact ⟨_, findEntry?_some_mem_toList h', findEntry?_some_eq_eq h'⟩
|
case intro.mk.intro
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
x : α
t : RBMap α β cmp
y : α
v : β
h' : findEntry? t x = some (y, v)
h : find? t x = some (y, v).snd
⊢ ∃ y_1, (y_1, (y, v).snd) ∈ toList t ∧ cmp x y_1 = Ordering.eq
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
simp [find?, findEntry?_some]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ find? t x = some v ↔ ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v) ↔ ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
constructor
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v) ↔ ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
|
case mp
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v) → ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
case mpr
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq) → ∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
rintro ⟨_, h, rfl⟩
|
case mp
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v) → ∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq
|
case mp.intro.intro
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
inst✝ : TransCmp cmp
t : RBMap α β cmp
w✝ : α × β
h : w✝ ∈ toList t ∧ cmp x w✝.fst = Ordering.eq
⊢ ∃ y, (y, w✝.snd) ∈ toList t ∧ cmp x y = Ordering.eq
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
exact ⟨_, h⟩
|
case mp.intro.intro
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
inst✝ : TransCmp cmp
t : RBMap α β cmp
w✝ : α × β
h : w✝ ∈ toList t ∧ cmp x w✝.fst = Ordering.eq
⊢ ∃ y, (y, w✝.snd) ∈ toList t ∧ cmp x y = Ordering.eq
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
rintro ⟨b, h⟩
|
case mpr
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ (∃ y, (y, v) ∈ toList t ∧ cmp x y = Ordering.eq) → ∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v
|
case mpr.intro
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
b : α
h : (b, v) ∈ toList t ∧ cmp x b = Ordering.eq
⊢ ∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_some
|
[165, 1]
|
[169, 37]
|
exact ⟨_, h, rfl⟩
|
case mpr.intro
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
x : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
b : α
h : (b, v) ∈ toList t ∧ cmp x b = Ordering.eq
⊢ ∃ a, (a ∈ toList t ∧ cmp x a.fst = Ordering.eq) ∧ a.snd = v
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.contains_iff_find?
|
[174, 1]
|
[176, 63]
|
simp [contains_iff_findEntry?, find?, and_comm, exists_comm]
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
x : α
t : RBMap α β cmp
⊢ contains t x = true ↔ ∃ v, find? t x = some v
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.findEntry?_congr
|
[190, 1]
|
[191, 90]
|
simp [findEntry?, TransCmp.cmp_congr_left' h]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k₁ k₂ : α
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k₁ k₂ = Ordering.eq
⊢ findEntry? t k₁ = findEntry? t k₂
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_congr
|
[193, 1]
|
[194, 69]
|
simp [find?, findEntry?_congr _ h]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k₁ k₂ : α
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k₁ k₂ = Ordering.eq
⊢ find? t k₁ = find? t k₂
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert_of_eq
|
[199, 1]
|
[200, 88]
|
rw [find?, findEntry?_insert_of_eq _ h]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k' k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k' k = Ordering.eq
⊢ find? (insert t k v) k' = some v
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k' k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k' k = Ordering.eq
⊢ Option.map (fun x => x.snd) (some (k, v)) = some v
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert_of_eq
|
[199, 1]
|
[200, 88]
|
rfl
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k' k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k' k = Ordering.eq
⊢ Option.map (fun x => x.snd) (some (k, v)) = some v
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert_of_ne
|
[205, 1]
|
[206, 89]
|
simp [find?, findEntry?_insert_of_ne _ h]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
k' k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k' k ≠ Ordering.eq
⊢ find? (insert t k v) k' = find? t k'
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert
|
[212, 1]
|
[214, 77]
|
split <;> [exact find?_insert_of_eq t ‹_›; exact find?_insert_of_ne t ‹_›]
|
α : Type u_1
cmp : α → α → Ordering
β : Type u_2
inst✝ : TransCmp cmp
t : RBMap α β cmp
k : α
v : β
k' : α
⊢ find? (insert t k v) k' = if cmp k' k = Ordering.eq then some v else find? t k'
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert_self
|
[221, 9]
|
[222, 106]
|
rw [find?_insert_of_eq]
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ find? (insert t k v) k = some v
|
case h
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ cmp k k = Ordering.eq
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.find?_insert_self
|
[221, 9]
|
[222, 106]
|
rw [OrientedCmp.cmp_refl (cmp := cmp)]
|
case h
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
⊢ cmp k k = Ordering.eq
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.findD_insert
|
[224, 1]
|
[226, 49]
|
simp only [findD, find?_insert]
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
inst✝ : TransCmp cmp
t : RBMap α β cmp
k : α
v : β
k' : α
d : β
⊢ findD (insert t k v) k' d = if cmp k' k = Ordering.eq then v else findD t k' d
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
inst✝ : TransCmp cmp
t : RBMap α β cmp
k : α
v : β
k' : α
d : β
⊢ Option.getD (if cmp k' k = Ordering.eq then some v else find? t k') d =
if cmp k' k = Ordering.eq then v else Option.getD (find? t k') d
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.findD_insert
|
[224, 1]
|
[226, 49]
|
split <;> rfl
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
inst✝ : TransCmp cmp
t : RBMap α β cmp
k : α
v : β
k' : α
d : β
⊢ Option.getD (if cmp k' k = Ordering.eq then some v else find? t k') d =
if cmp k' k = Ordering.eq then v else Option.getD (find? t k') d
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.findD_insert_self
|
[228, 9]
|
[229, 52]
|
simp [findD]
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
d : β
⊢ findD (insert t k v) k d = v
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/Verification/RBMap.lean
|
Std.RBMap.findD_insert_of_ne
|
[231, 1]
|
[232, 74]
|
simp [findD_insert, h]
|
α : Type u_1
β : Type u_2
cmp : α → α → Ordering
k' k : α
v : β
inst✝ : TransCmp cmp
t : RBMap α β cmp
h : cmp k' k ≠ Ordering.eq
d : β
⊢ findD (insert t k v) k' d = findD t k' d
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_map
|
[34, 1]
|
[37, 21]
|
dsimp [Stream.eval₀]
|
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
q : { q // s.valid q = true }
inst✝¹ : Zero α
inst✝ : Zero β
f : α → β
hf : f 0 = 0
⊢ eval₀ (map f s) q = Finsupp.mapRange f hf (eval₀ s q)
|
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
q : { q // s.valid q = true }
inst✝¹ : Zero α
inst✝ : Zero β
f : α → β
hf : f 0 = 0
⊢ (if h₂ : s.ready q = true then fun₀ | s.index q => f (s.value { val := q, property := h₂ }) else 0) =
Finsupp.mapRange f hf
(if h₂ : s.ready q = true then fun₀ | s.index q => s.value { val := q, property := h₂ } else 0)
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval₀_map
|
[34, 1]
|
[37, 21]
|
split_ifs <;> simp
|
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
q : { q // s.valid q = true }
inst✝¹ : Zero α
inst✝ : Zero β
f : α → β
hf : f 0 = 0
⊢ (if h₂ : s.ready q = true then fun₀ | s.index q => f (s.value { val := q, property := h₂ }) else 0) =
Finsupp.mapRange f hf
(if h₂ : s.ready q = true then fun₀ | s.index q => s.value { val := q, property := h₂ } else 0)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_zero
|
[47, 1]
|
[51, 10]
|
ext <;> try rfl
|
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ map f 0 = 0
|
case value
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ HEq (map f 0).value 0.value
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_zero
|
[47, 1]
|
[51, 10]
|
rw [heq_iff_eq]
|
case value
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ HEq (map f 0).value 0.value
|
case value
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ (map f 0).value = 0.value
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_zero
|
[47, 1]
|
[51, 10]
|
funext ⟨q, h⟩
|
case value
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ (map f 0).value = 0.value
|
case value.h
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
q : { x // (map f 0).valid x = true }
h : (map f 0).ready q = true
⊢ (map f 0).value { val := q, property := h } = 0.value { val := q, property := h }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_zero
|
[47, 1]
|
[51, 10]
|
cases h
|
case value.h
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
q : { x // (map f 0).valid x = true }
h : (map f 0).ready q = true
⊢ (map f 0).value { val := q, property := h } = 0.value { val := q, property := h }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.map_zero
|
[47, 1]
|
[51, 10]
|
rfl
|
case ready
ι : Type
α : Type u_2
a b s : Stream ι α
β : Type u_1
f : α → β
⊢ HEq (map f 0).ready 0.ready
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.ready'_val
|
[64, 1]
|
[65, 34]
|
simp [Stream.ready', x.prop]
|
ι : Type
α : Type u_1
a b s : Stream ι α
x : { q // s.valid q = true }
⊢ ready' s ↑x ↔ s.ready x = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.coeLex_le_iff
|
[91, 1]
|
[92, 26]
|
simp [Prod.Lex.le_iff']
|
ι : Type
α : Type ?u.4823
a b s : Stream ι α
inst✝ : Preorder ι
x y : StreamOrder ι
⊢ coeLex x ≤ coeLex y ↔ x ≤ y
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.coeLex_lt_iff
|
[95, 1]
|
[96, 26]
|
simp [Prod.Lex.lt_iff']
|
ι : Type
α : Type ?u.6775
a b s : Stream ι α
inst✝ : Preorder ι
x y : StreamOrder ι
⊢ coeLex x < coeLex y ↔ x < y
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.coeLex_injective
|
[98, 1]
|
[101, 9]
|
rw [Prod.mk.injEq .., Prod.mk.injEq ..]
|
ι : Type
α : Type ?u.7590
a b s : Stream ι α
x₁ : ι
y₁ : Bool
x₂ : ι
y₂ : Bool
⊢ coeLex (x₁, y₁) = coeLex (x₂, y₂) → (x₁, y₁) = (x₂, y₂)
|
ι : Type
α : Type ?u.7590
a b s : Stream ι α
x₁ : ι
y₁ : Bool
x₂ : ι
y₂ : Bool
⊢ ↑(x₁, y₁).1 = ↑(x₂, y₂).1 ∧ (x₁, y₁).2 = (x₂, y₂).2 → x₁ = x₂ ∧ y₁ = y₂
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.coeLex_injective
|
[98, 1]
|
[101, 9]
|
simp
|
ι : Type
α : Type ?u.7590
a b s : Stream ι α
x₁ : ι
y₁ : Bool
x₂ : ι
y₂ : Bool
⊢ ↑(x₁, y₁).1 = ↑(x₂, y₂).1 ∧ (x₁, y₁).2 = (x₂, y₂).2 → x₁ = x₂ ∧ y₁ = y₂
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.index'_invalid
|
[118, 1]
|
[119, 21]
|
simpa
|
ι : Type
α : Type u_1
a b s : Stream ι α
x : s.σ
h : s.valid x = false
⊢ ¬s.valid x = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.toOrder'_val
|
[152, 1]
|
[153, 72]
|
simp [Stream.toOrder']
|
ι : Type
α : Type u_1
a b s : Stream ι α
q : { q // s.valid q = true }
⊢ toOrder' s ↑q = (index' s ↑q, s.ready q)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.coeLex_toOrder
|
[155, 1]
|
[157, 37]
|
simp [coeLex, Stream.toOrder'_val]
|
ι : Type
α : Type u_1
a b s : Stream ι α
q : { q // s.valid q = true }
⊢ toOrder' s ↑q = coeLex (toOrder s q)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.toOrder'_val_snd
|
[160, 1]
|
[161, 66]
|
simp [Stream.toOrder'_val]
|
ι : Type
α : Type u_1
a b s : Stream ι α
q : { q // s.valid q = true }
⊢ (toOrder' s ↑q).2 = s.ready q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.index'_lt_top_iff
|
[165, 1]
|
[170, 13]
|
rw [Stream.index']
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
⊢ index' s q < ⊤ ↔ s.valid q = true
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
⊢ (if h : s.valid q = true then ↑(s.index { val := q, property := h }) else ⊤) < ⊤ ↔ s.valid q = true
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.index'_lt_top_iff
|
[165, 1]
|
[170, 13]
|
split_ifs
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
⊢ (if h : s.valid q = true then ↑(s.index { val := q, property := h }) else ⊤) < ⊤ ↔ s.valid q = true
|
case pos
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
h✝ : s.valid q = true
⊢ ↑(s.index { val := q, property := h✝ }) < ⊤ ↔ s.valid q = true
case neg
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
h✝ : ¬s.valid q = true
⊢ ⊤ < ⊤ ↔ s.valid q = true
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.index'_lt_top_iff
|
[165, 1]
|
[170, 13]
|
simpa [WithTop.coe_lt_top]
|
case pos
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
h✝ : s.valid q = true
⊢ ↑(s.index { val := q, property := h✝ }) < ⊤ ↔ s.valid q = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.index'_lt_top_iff
|
[165, 1]
|
[170, 13]
|
simp [*]
|
case neg
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
q : s.σ
h✝ : ¬s.valid q = true
⊢ ⊤ < ⊤ ↔ s.valid q = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.get_index'
|
[173, 1]
|
[176, 42]
|
simpa using h
|
ι : Type
α : Type ?u.13400
a b s : Stream ι α
inst✝ : PartialOrder ι
x : s.σ
h : Option.isSome (index' s x) = true
⊢ s.valid x = true
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.get_index'
|
[173, 1]
|
[176, 42]
|
generalize_proofs hq
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : PartialOrder ι
x : s.σ
h : Option.isSome (index' s x) = true
⊢ Option.get (index' s x) h = s.index { val := x, property := ⋯ }
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : PartialOrder ι
x : s.σ
h : Option.isSome (index' s x) = true
hq : s.valid x = true
⊢ Option.get (index' s x) h = s.index { val := x, property := hq }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.get_index'
|
[173, 1]
|
[176, 42]
|
simp_rw [Stream.index', hq, Option.get]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : PartialOrder ι
x : s.σ
h : Option.isSome (index' s x) = true
hq : s.valid x = true
⊢ Option.get (index' s x) h = s.index { val := x, property := hq }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.wf_valid_iff
|
[219, 1]
|
[222, 79]
|
simp only [Stream.seek'_val q.prop, Stream.coeLex_toOrder, coeLex_lt_iff]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
wf_rel : s.σ → s.σ → Prop
q : { x // s.valid x = true }
i : Lex (ι × Bool)
⊢ wf_rel (s.seek q i) ↑q ∨ i < Stream.toOrder s q ∧ s.seek q i = ↑q ↔
wf_rel (Stream.seek' s (↑q) i) ↑q ∨ coeLex i < Stream.toOrder' s ↑q ∧ Stream.seek' s (↑q) i = ↑q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.IsBounded.mk'
|
[225, 1]
|
[233, 36]
|
simp only [wf_valid_iff]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
h :
∃ wf_rel,
∀ (q : s.σ) (i : StreamOrder ι),
WellFoundedRelation.rel (Stream.seek' s q i) q ∨ coeLex i < Stream.toOrder' s q ∧ Stream.seek' s q i = q
⊢ ∃ wf_rel,
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)),
WellFoundedRelation.rel (s.seek q i) ↑q ∨ i < Stream.toOrder s q ∧ s.seek q i = ↑q
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
h :
∃ wf_rel,
∀ (q : s.σ) (i : StreamOrder ι),
WellFoundedRelation.rel (Stream.seek' s q i) q ∨ coeLex i < Stream.toOrder' s q ∧ Stream.seek' s q i = q
⊢ ∃ wf_rel,
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)),
WellFoundedRelation.rel (Stream.seek' s (↑q) i) ↑q ∨ coeLex i < Stream.toOrder' s ↑q ∧ Stream.seek' s (↑q) i = ↑q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.IsBounded.mk'
|
[225, 1]
|
[233, 36]
|
rcases h with ⟨wfr, hr⟩
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
h :
∃ wf_rel,
∀ (q : s.σ) (i : StreamOrder ι),
WellFoundedRelation.rel (Stream.seek' s q i) q ∨ coeLex i < Stream.toOrder' s q ∧ Stream.seek' s q i = q
⊢ ∃ wf_rel,
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)),
WellFoundedRelation.rel (Stream.seek' s (↑q) i) ↑q ∨ coeLex i < Stream.toOrder' s ↑q ∧ Stream.seek' s (↑q) i = ↑q
|
case intro
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
wfr : WellFoundedRelation s.σ
hr :
∀ (q : s.σ) (i : StreamOrder ι),
WellFoundedRelation.rel (Stream.seek' s q i) q ∨ coeLex i < Stream.toOrder' s q ∧ Stream.seek' s q i = q
⊢ ∃ wf_rel,
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)),
WellFoundedRelation.rel (Stream.seek' s (↑q) i) ↑q ∨ coeLex i < Stream.toOrder' s ↑q ∧ Stream.seek' s (↑q) i = ↑q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.IsBounded.mk'
|
[225, 1]
|
[233, 36]
|
exact ⟨wfr, fun q i => hr q i⟩
|
case intro
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝ : Preorder ι
wfr : WellFoundedRelation s.σ
hr :
∀ (q : s.σ) (i : StreamOrder ι),
WellFoundedRelation.rel (Stream.seek' s q i) q ∨ coeLex i < Stream.toOrder' s q ∧ Stream.seek' s q i = q
⊢ ∃ wf_rel,
∀ (q : { x // s.valid x = true }) (i : Lex (ι × Bool)),
WellFoundedRelation.rel (Stream.seek' s (↑q) i) ↑q ∨ coeLex i < Stream.toOrder' s ↑q ∧ Stream.seek' s (↑q) i = ↑q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
rw [← wf_valid_iff (q := ⟨q, hq⟩)]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : s.valid q = true
⊢ WfRel s (seek' s q i) q ∨ coeLex i < toOrder' s q ∧ seek' s q i = q
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : s.valid q = true
⊢ WfRel s (s.seek { val := q, property := hq } i) ↑{ val := q, property := hq } ∨
i < toOrder s { val := q, property := hq } ∧ s.seek { val := q, property := hq } i = ↑{ val := q, property := hq }
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
exact s.wf_valid ⟨q, hq⟩ i
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : s.valid q = true
⊢ WfRel s (s.seek { val := q, property := hq } i) ↑{ val := q, property := hq } ∨
i < toOrder s { val := q, property := hq } ∧ s.seek { val := q, property := hq } i = ↑{ val := q, property := hq }
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
right
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ WfRel s (seek' s q i) q ∨ coeLex i < toOrder' s q ∧ seek' s q i = q
|
case h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ coeLex i < toOrder' s q ∧ seek' s q i = q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
constructor
|
case h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ coeLex i < toOrder' s q ∧ seek' s q i = q
|
case h.left
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ coeLex i < toOrder' s q
case h.right
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ seek' s q i = q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
rw [Prod.Lex.lt_iff']
|
case h.left
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ coeLex i < toOrder' s q
|
case h.left
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ (coeLex i).1 < (toOrder' s q).1 ∨ (coeLex i).1 = (toOrder' s q).1 ∧ (coeLex i).2 < (toOrder' s q).2
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
left
|
case h.left
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ (coeLex i).1 < (toOrder' s q).1 ∨ (coeLex i).1 = (toOrder' s q).1 ∧ (coeLex i).2 < (toOrder' s q).2
|
case h.left.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ (coeLex i).1 < (toOrder' s q).1
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
simp [hq]
|
case h.left.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ (coeLex i).1 < (toOrder' s q).1
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.wf_valid'
|
[236, 1]
|
[247, 16]
|
simp [hq]
|
case h.right
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : s.σ
i : StreamOrder ι
hq : ¬s.valid q = true
⊢ seek' s q i = q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.next_wf
|
[253, 1]
|
[255, 26]
|
rw [Stream.advance_val]
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : { q // s.valid q = true }
⊢ WfRel s (advance s ↑q) ↑q
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : { q // s.valid q = true }
⊢ WfRel s (s.seek q (toOrder s q)) ↑q
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.next_wf
|
[253, 1]
|
[255, 26]
|
exact s.progress rfl.le
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : IsBounded s
q : { q // s.valid q = true }
⊢ WfRel s (s.seek q (toOrder s q)) ↑q
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_zero
|
[275, 1]
|
[276, 30]
|
ext
|
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : AddZeroClass α
⊢ eval 0 = 0
|
case h.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : AddZeroClass α
x✝ : 0.σ
a✝ : ι
⊢ (eval 0 x✝) a✝ = (0 x✝) a✝
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_zero
|
[275, 1]
|
[276, 30]
|
rw [Stream.eval]
|
case h.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : AddZeroClass α
x✝ : 0.σ
a✝ : ι
⊢ (eval 0 x✝) a✝ = (0 x✝) a✝
|
case h.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : AddZeroClass α
x✝ : 0.σ
a✝ : ι
⊢ (if h : 0.valid x✝ = true then
let_fun this := ⋯;
eval₀ 0 { val := x✝, property := h } + eval 0 (advance 0 x✝)
else 0)
a✝ =
(0 x✝) a✝
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_zero
|
[275, 1]
|
[276, 30]
|
simp
|
case h.h
ι : Type
α : Type u_1
a b s : Stream ι α
inst✝¹ : Preorder ι
inst✝ : AddZeroClass α
x✝ : 0.σ
a✝ : ι
⊢ (if h : 0.valid x✝ = true then
let_fun this := ⋯;
eval₀ 0 { val := x✝, property := h } + eval 0 (advance 0 x✝)
else 0)
a✝ =
(0 x✝) a✝
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_invalid
|
[279, 1]
|
[281, 67]
|
rwa [Stream.eval, dif_neg]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
q : s.σ
h : ¬s.valid q = true
⊢ eval s q = 0
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_valid
|
[284, 1]
|
[286, 78]
|
rw [Stream.eval, dif_pos]
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
q : { q // s.valid q = true }
⊢ eval s ↑q = eval₀ s q + eval s (advance s ↑q)
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map_id
|
[289, 1]
|
[290, 47]
|
subst f
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddZeroClass α
f : α → α
hf : f = id
s : Stream ι α
inst✝ : IsBounded s
⊢ eval (map f s) = eval s
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
⊢ eval (map id s) = eval s
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map_id
|
[289, 1]
|
[290, 47]
|
rfl
|
ι : Type
α : Type u_1
a b s✝ : Stream ι α
inst✝² : Preorder ι
inst✝¹ : AddZeroClass α
s : Stream ι α
inst✝ : IsBounded s
⊢ eval (map id s) = eval s
|
no goals
|
https://github.com/kovach/etch.git
|
b9e66fe99c33dc1edd926626e598ba00d5d78627
|
Etch/StreamFusion/Proofs/StreamProof.lean
|
Etch.Verification.Stream.eval_map
|
[292, 1]
|
[302, 49]
|
apply s.wf.induction 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
⊢ eval (map (⇑f) s) q = (Finsupp.mapRange.addMonoidHom f) (eval s 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)
|
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