case _ c1 =>
  exact E_ih h2 V a
D : Type
I : Interpretation D
M : MetaValuation D
Γ : List (VarName × MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v ∉ xs
h2 : ∀ (X : MetaVarName), (v, X) ∈ Γ → ∀ (V : Valuation D) (d : D), M X V ↔ M X (Function.updateITE V v d)
E_ih :
  (∀ (X : MetaVarName), (v, X) ∈ Γ → ∀ (V : Valuation D) (d : D), M X V ↔ M X (Function.updateITE V v d)) →
    ∀ (V : Valuation D) (d : D),
      Holds D I V M E_tl (def_ X xs) ↔ Holds D I (Function.updateITE V v d) M E_tl (def_ X xs)
V : Valuation D
a : D
c1 : ¬(X = E_hd.name ∧ xs.length = E_hd.args.length)
⊢ Holds D I V M E_tl (def_ X xs) ↔ Holds D I (Function.updateITE V v a) M E_tl (def_ X xs)
no goals