assumption
case intro
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α✝ σ✝ : Type
ε✝ : σ✝ → Type
Δ : Dialect α✝ σ✝ ε✝
S : Semantics Δ
head : TypedSSAVal Δ
tail : List (TypedSSAVal Δ)
env : SSAEnv Δ
r✝ : List (TypedArg Δ)
headName : SSAVal
headτ : MLIRType Δ
r : MLIRType.eval headτ × SSAEnv Δ
rRes : MLIRType.eval headτ
left✝¹ :
  (match SSAEnv.get headName headτ env with
    | some v => v
    | none => default) =
    rRes
x✝ : Except (String × SSAEnv Δ) (List (TypedArg Δ) × SSAEnv Δ)
tailR : List (TypedArg Δ) × SSAEnv Δ
tailRes : List (TypedArg Δ)
tailEnv : SSAEnv Δ
HTailR :
  mapM
      (fun x s =>
        match TopM.get x.snd x.fst s with
        | Except.error err => Except.error err
        | Except.ok v => Except.ok ({ fst := x.snd, snd := v.fst }, v.snd))
      tail env =
    Except.ok (tailRes, tailEnv)
HInd : tailEnv = env
left✝ : { fst := headτ, snd := rRes } :: tailRes = r✝
⊢ tailEnv = env
no goals