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/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_ne_type | [207, 1] | [218, 50] | simp | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (set v τ' val... | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (if head.fst ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_ne_type | [207, 1] | [218, 50] | byCases H: head.fst = v | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (if head.fst ... | case cons.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get head.fst (set head.fst τ' val tail) τ = none
⊢ τ' = τ → Fals... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_ne_type | [207, 1] | [218, 50] | . simp [Hne] | case cons.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get head.fst (set head.fst τ' val tail) τ = none
⊢ τ' = τ → Fals... | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_ne_type | [207, 1] | [218, 50] | . byCases H2: head.fst = v <;> try assumption | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_ne_type | [207, 1] | [218, 50] | assumption | case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H H2 : ¬head.fs... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_eq | [220, 1] | [227, 15] | induction scope with
| nil => simp;
| cons head nil =>
simp
byCases H: head.fst = v <;> try apply cast_eq
assumption | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
scope : SSAScope δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v (set v τ val scope) τ = some val | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_eq | [220, 1] | [227, 15] | simp | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v (set v τ val []) τ = some val | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_eq | [220, 1] | [227, 15] | simp | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (set v τ val (head :: nil... | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (if head.fst = v then (he... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_eq | [220, 1] | [227, 15] | byCases H: head.fst = v <;> try apply cast_eq | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (if head.fst = v then (he... | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
H : ¬head.fst = v
⊢ get v (set... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.get_set_eq | [220, 1] | [227, 15] | assumption | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
H : ¬head.fst = v
⊢ get v (set... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | intros Hne scope τ τ' val val' | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v →
∀ ⦃scope : SSAScope δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄ ⦃val' : MLIRType.eval τ'⦄,
equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope)) | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
scope : SSAScope δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope)) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | induction scope with
| nil =>
simp; simp [Hne, Hne.symm]
simp [equiv]; intros name τ''
byCases Hv: v' = name
byCases Hτ: τ' = τ'' <;> simp [Hne.symm]
| cons head tail Hind =>
simp [equiv] at *
intros name; specialize Hind name
simp at *
byCases Hv': head.fst = v' <;> simp [Hne]
byCases Hv: head.fst = ... | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
scope : SSAScope δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope)) | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | simp | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' [])) (set v' τ' val' (set v τ val [])) | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv
(if v' = v then [(v', { fst := τ, snd := val })]
else [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })])
(if v ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | simp [Hne, Hne.symm] | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv
(if v' = v then [(v', { fst := τ, snd := val })]
else [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })])
(if v ... | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })]
[(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })] |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | simp [equiv] | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })]
[(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })] | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
(if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | intros name τ'' | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
(if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
... | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
⊢ (if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | byCases Hv: v' = name | case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
⊢ (if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ... | case nil.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
Hne : name ≠ v
⊢ (if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRTyp... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | byCases Hτ: τ' = τ'' <;> simp [Hne.symm] | case nil.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
Hne : name ≠ v
⊢ (if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRTyp... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | simp [equiv] at * | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : equiv (set v τ val (set v' τ' ... | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : ML... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | intros name | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : ML... | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : ML... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | specialize Hind name | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : ML... | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIR... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | byCases Hv': head.fst = v' <;> simp [Hne] | case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIR... | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : M... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | byCases Hv: head.fst = v <;> simp [Hv'] | case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : M... | case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAScope.set_commutes | [229, 1] | [246, 50] | byCases Hname: head.fst = name <;> assumption | case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 ... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_rfl | [309, 1] | [310, 38] | intros v τ | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
⊢ equiv env env | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
⊢ get v τ env = get v τ env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_rfl | [309, 1] | [310, 38] | rfl | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
⊢ get v τ env = get v τ env | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_symm | [312, 1] | [316, 11] | intros H name | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
⊢ equiv env env' → equiv env' env | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
H : equiv env env'
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_symm | [312, 1] | [316, 11] | specialize H name | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
H : equiv env env'
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
name : SSAVal
H : ∀ (τ : MLIRType δ), get name τ env = get name τ env'
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_symm | [312, 1] | [316, 11] | simp [H] | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
name : SSAVal
H : ∀ (τ : MLIRType δ), get name τ env = get name τ env'
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_trans | [318, 1] | [325, 16] | intros _ _ H1 _ H2 name | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
⊢ ∀ ⦃env₁ env₂ : SSAEnv δ⦄, equiv env₁ env₂ → ∀ ⦃env₃ : SSAEnv δ⦄, equiv env₂ env₃ → equiv env₁ env₃ | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ : SSAEnv δ
H1 : equiv env₁✝ env₂✝
env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_trans | [318, 1] | [325, 16] | specialize H1 name | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ : SSAEnv δ
H1 : equiv env₁✝ env₂✝
env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_trans | [318, 1] | [325, 16] | specialize H2 name | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
H2 : ∀ (τ : MLIRType δ), get name τ env₂✝ = get name τ env₃✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_trans | [318, 1] | [325, 16] | simp [H1, H2] | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
H2 : ∀ (τ : MLIRType δ), get name τ env₂✝ = get name τ env₃✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝ | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | intros Hne env τ val | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v → ∀ ⦃env : SSAEnv δ⦄ ⦃τ : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄, getT v (set v' τ val env) = getT v env | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v' τ val env) = getT v env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | cases env with
| One s =>
simp [getT, set]
rw [SSAScope.getT_set_ne]
assumption
| Cons head tail =>
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
rw [SSAScope.getT_set_ne]
assumption | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v' τ val env) = getT v env | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | simp [getT, set] | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ getT v (set v' τ val (One s)) = getT v (One s) | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v' τ val s) = SSAScope.getT v s |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | rw [SSAScope.getT_set_ne] | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v' τ val s) = SSAScope.getT v s | case One.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ v' ≠ v |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | assumption | case One.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ v' ≠ v | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse] | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ getT v (set v' τ val (Cons head tail)) = getT v (Cons head tail) | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v' τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
mat... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | rw [SSAScope.getT_set_ne] | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v' τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
mat... | case Cons.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ v' ≠ v |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_ne | [327, 1] | [340, 15] | assumption | case Cons.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ v' ≠ v | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_eq | [342, 1] | [350, 32] | cases env with
| One s =>
simp [getT, set]
rw [SSAScope.getT_set_eq]
| Cons head tail =>
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
simp [SSAScope.getT_set_eq] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v τ val env) = some { fst := τ, snd := val } | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_eq | [342, 1] | [350, 32] | simp [getT, set] | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ getT v (set v τ val (One s)) = some { fst := τ, snd := val } | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v τ val s) = some { fst := τ, snd := val } |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_eq | [342, 1] | [350, 32] | rw [SSAScope.getT_set_eq] | case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v τ val s) = some { fst := τ, snd := val } | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_eq | [342, 1] | [350, 32] | simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse] | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ getT v (set v τ val (Cons head tail)) = some { fst := τ, snd := val } | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
some { fst := τ, snd... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.getT_set_eq | [342, 1] | [350, 32] | simp [SSAScope.getT_set_eq] | case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
some { fst := τ, snd... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_ne_val | [352, 1] | [359, 13] | intros Hne env τ τ' val | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v → ∀ ⦃env : SSAEnv δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ'⦄, get v τ (set v' τ' val env) = get v τ env | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) = get v τ env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_ne_val | [352, 1] | [359, 13] | simp [get] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) = get v τ env | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ (match getT v (set v' τ' val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_ne_val | [352, 1] | [359, 13] | rw [SSAEnv.getT_set_ne] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ (match getT v (set v' τ' val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
... | case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ v' ≠ v |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_ne_val | [352, 1] | [359, 13] | assumption | case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ v' ≠ v | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_eq_val | [361, 1] | [368, 26] | simp [H'] | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
H' : τ' = τ
⊢ MLIRType.eval τ' = MLIRType.eval τ | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_eq_val | [361, 1] | [368, 26] | simp [get, getT_set_eq] | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if H' : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => F... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set | [370, 1] | [383, 15] | simp [H] | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : τ' = τ
⊢ MLIRType.eval τ' = MLIRType.eval τ | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set | [370, 1] | [383, 15] | byCases H: v' = v | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) =
if v' = v then
if H : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
... | case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set | [370, 1] | [383, 15] | . simp [get_set_eq_val] | case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness ... | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set | [370, 1] | [383, 15] | . rw [get_set_ne_val]
assumption | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_eq | [385, 1] | [387, 26] | simp [get, getT_set_eq] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v τ (set v τ val env) = some val | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_neq | [389, 1] | [392, 42] | simp[get] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v τ (set v' τ val env) = get v τ env | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ (match getT v (set v' τ val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_neq | [389, 1] | [392, 42] | rw[SSAEnv.getT_set_ne] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ (match getT v (set v' τ val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :... | case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_neq | [389, 1] | [392, 42] | try assumption; | case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.get_set_neq | [389, 1] | [392, 42] | assumption | case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | intros HEnv name τ v name' τ' | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
⊢ equiv env₁ env₂ →
∀ ⦃name : SSAVal⦄ ⦃τ : MLIRType δ⦄ ⦃v : MLIRType.eval τ⦄, equiv (set name τ v env₁) (set name τ v env₂) | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | byCases Hname: name = name' | α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂) | case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name' τ v env₁) = get name' τ' (set name' τ v env₂)
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | . simp [get_set_eq_val] | case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name' τ v env₁) = get name' τ' (set name' τ v env₂)
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env... | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | . repeat rw [get_set_ne_val] <;> try assumption
apply HEnv | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂) | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | rw [get_set_ne_val] <;> try assumption | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' env₁ = get name' τ' (set name τ v env₂) | case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' env₁ = get name' τ' env₂ |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.equiv_set | [394, 1] | [401, 15] | assumption | case h2.a
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ name ≠ name' | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | intros Hne env τ τ' val val' v₂ τ₂ | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v →
∀ ⦃env : SSAEnv δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄ ⦃val' : MLIRType.eval τ'⦄,
equiv (set v τ val (set v' τ' val' env)) (set v' τ' val' (set v τ val env)) | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ get v₂ τ₂ (set v τ val (set v' τ' val' env)) = get v₂ τ₂ (set v' τ' val' (set v τ val env)) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | repeat rw [get_set] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ get v₂ τ₂ (set v τ val (set v' τ' val' env)) = get v₂ τ₂ (set v' τ' val' (set v τ val env)) | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ w... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | split | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ w... | case inl
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : v = v₂
⊢ (if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | . subst v
simp [Hne] | case inl
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : v = v₂
⊢ (if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
... | case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | . split <;> simp | case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | SSAEnv.set_commutes | [403, 1] | [412, 19] | rw [get_set] | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ w... | α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ w... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | interpSSA'_trigger_MemberSumL | [499, 9] | [503, 34] | simp [Fitree.trigger, pair_eta] | α σ : Type
ε : σ → Type
α' σ' : Type
ε' : σ' → Type
T : Type
E : Type → Type
Δ : Dialect α' σ' ε'
e : SSAEnvE Δ T
s₁ : SSAEnv Δ
⊢ interpSSA' (Fitree.trigger e) s₁ = SSAEnvE.handle T e s₁ | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/SSAEnv.lean | interpSSA'_bind | [505, 1] | [510, 32] | apply Fitree.interpState_bind | α σ : Type
ε : σ → Type
E : Type → Type
T R : Type
δ : Dialect α σ ε
t : Fitree (SSAEnvE δ +' E) T
k : T → Fitree (SSAEnvE δ +' E) R
s₁ : SSAEnv δ
⊢ interpSSA' (Fitree.bind t k) s₁ =
Fitree.bind (interpSSA' t s₁) fun x =>
match x with
| (x, s₂) => interpSSA' (k x) s₂ | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | BubbleUpExtractSlice.bubble_up_extract_slice | [145, 1] | [151, 2] | cases t | M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
t : Tensor1D
f : FinInt 32 → M (FinInt 32)
⊢ (fun s => Tensor1D.extract s len) <$> Tensor1D.mapM t f = Tensor1D.mapM (Tensor1D.extract t len) f | case mk
M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
f : FinInt 32 → M (FinInt 32)
size0✝ : ℕ
data✝ : List (FinInt 32)
h_data_size✝ : List.length data✝ = size0✝
⊢ (fun s => Tensor1D.extract s len) <$>
Tensor1D.mapM { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } f =
Tensor1D.mapM (T... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | BubbleUpExtractSlice.bubble_up_extract_slice | [145, 1] | [151, 2] | sorry | case mk
M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
f : FinInt 32 → M (FinInt 32)
size0✝ : ℕ
data✝ : List (FinInt 32)
h_data_size✝ : List.length data✝ = size0✝
⊢ (fun s => Tensor1D.extract s len) <$>
Tensor1D.mapM { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } f =
Tensor1D.mapM (T... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | simp [Tensor1D.fill, Tensor1D.extract] | t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ Tensor1D.fill (Tensor1D.extract t extractlen) fillval = Tensor1D.extract (Tensor1D.fill t fillval) extractlen | t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.replicate (min extractlen t.size0) fillval = List.take extractlen (List.replicate t.size0 fillval) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | apply List.extF | t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.replicate (min extractlen t.size0) fillval = List.take extractlen (List.replicate t.size0 fillval) | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ ∀ (n : ℕ) (h : n < List.length (List.replicate (min extractlen t.size0) fillval)),
List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.t... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | intros n h | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ ∀ (n : ℕ) (h : n < List.length (List.replicate (min extractlen t.size0) fillval)),
List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.t... | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | simp | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen ... | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : T... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | simp at h | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : T... | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h✝ : n < List.length (List.replicate (min extractlen t.size0) fillval)
h : n < extractlen ∧ n < t.size0
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h✝ =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | sorry | case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h✝ : n < List.length (List.replicate (min extractlen t.size0) fillval)
h : n < extractlen ∧ n < t.size0
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h✝ =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate ... | case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval)) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceFillCommuteOneD.extract_fill_commute | [181, 1] | [195, 3] | sorry | case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval)) | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceGenericCommute1D.equiv | [248, 1] | [264, 6] | intros valid_r | r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
⊢ validGenericRegion r rSpec →
run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) | r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceGenericCommute1D.equiv | [248, 1] | [264, 6] | simp[LHS, RHS] | r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) | r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | ExtractSliceGenericCommute1D.equiv | [248, 1] | [264, 6] | sorry | r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] ... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_cons | [270, 1] | [274, 2] | simp[List.mapM, List.mapM.loop] | m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ mapM f (x :: xs) = do
let b_1 ← f x
let bs ← mapM f xs
pure (b_1 :: bs) | m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ (do
let __do_lift ← f x
List.mapM.loop f xs [__do_lift]) =
do
let b_1 ← f x
let bs ← List.mapM.loop f xs []
pure (b_1 :: bs) |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_cons | [270, 1] | [274, 2] | sorry | m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ (do
let __do_lift ← f x
List.mapM.loop f xs [__do_lift]) =
do
let b_1 ← f x
let bs ← List.mapM.loop f xs []
pure (b_1 :: bs) | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.commute_implies_mapM_commute | [275, 1] | [280, 107] | sorry | m : Type → Type u_1
a b : Type
xs : List a
y : a
inst✝¹ : Monad m
inst✝ : LawfulMonad m
f g : a → m a
k : List a → a → m b
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ (do
l... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | funext x | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) = mapM (fish f g) | case h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
x : List a
⊢ fish (mapM f) (mapM g) x = mapM (fish f g)... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | induction x | case h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
x : List a
⊢ fish (mapM f) (mapM g) x = mapM (fish f g)... | case h.nil
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) []
c... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | case nil => {
simp[fish, List.mapM, List.mapM.loop];
} | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) [] | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | case cons head tail IH => {
rewrite [mapM_cons];
simp[fish];
simp [bind_assoc]
simp[mapM_cons];
congr; funext x';
rewrite [commute_implies_mapM_commute];
congr;
funext x';
simp [fish] at IH;
rewrite [<- IH];
simp[bind_assoc];
apply COMMUTE;
} | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | simp[fish, List.mapM, List.mapM.loop] | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) [] | no goals |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | rewrite [mapM_cons] | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | simp[fish] | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | congr | m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM... | case e_a
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) ta... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | funext x' | case e_a
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) ta... | case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) ... |
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/LinalgSemantics.lean | mapMCommute.mapM_commute | [282, 1] | [312, 2] | rewrite [commute_implies_mapM_commute] | case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) ... | case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) ... |
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