tauto
case h1.h2
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
hd : Definition
tl : List Definition
ih :
  ∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
    fastAdmitsAux v t binders F →
      (∀ v ∉ binders, V' v = V v) →
        (Holds D I (Function.updateITE V v (V' t)) tl F ↔ Holds D I V tl (fastReplaceFree v t F))
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : v ∈ xs → t ∉ binders
h2 : ∀ v ∉ binders, V' v = V v
v' : VarName
a1 : isFreeIn v' hd.q
s1 : List.map (fun x => if v = x then V' t else V x) xs = List.map (V ∘ fun x => if v = x then t else x) xs
c1 : X = hd.name ∧ xs.length = hd.args.length
⊢ hd.args.length = xs.length
no goals