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 : MLIRType δ),
    get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
name : SSAVal
⊢ ∀ (τ_1 : MLIRType δ),
    get name
        (set v τ val
          (if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
        τ_1 =
      get name
        (set v' τ' val'
          (if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
        τ_1
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 : MLIRType δ),
    get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
⊢ ∀ (τ_1 : MLIRType δ),
    get name
        (set v τ val
          (if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
        τ_1 =
      get name
        (set v' τ' val'
          (if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
        τ_1