case pred_ X xs =>
  unfold NoMetaVarAndAllFreeInList at h1
  simp only [Holds]
  congr! 1
  simp only [List.map_eq_map_iff]
  tauto
D : Type
I : Interpretation D
M : MetaValuation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
  ∀ (V V' : Valuation D) (F : Formula) (vs : List VarName),
    NoMetaVarAndAllFreeInList vs F → (∀ v ∈ vs, V v = V' v) → (Holds D I V M tail✝ F ↔ Holds D I V' M tail✝ F)
X : PredName
xs : List VarName
V V' : Valuation D
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
h2 : ∀ v ∈ vs, V v = V' v
⊢ Holds D I V M (head✝ :: tail✝) (pred_ X xs) ↔ Holds D I V' M (head✝ :: tail✝) (pred_ X xs)
no goals