exact psi_ih V V' vs h1_right h2
case a.h'.a
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)
phi psi : Formula
phi_ih :
  ∀ (V V' : Valuation D) (vs : List VarName),
    NoMetaVarAndAllFreeInList vs phi →
      (∀ v ∈ vs, V v = V' v) → (Holds D I V M (head✝ :: tail✝) phi ↔ Holds D I V' M (head✝ :: tail✝) phi)
psi_ih :
  ∀ (V V' : Valuation D) (vs : List VarName),
    NoMetaVarAndAllFreeInList vs psi →
      (∀ v ∈ vs, V v = V' v) → (Holds D I V M (head✝ :: tail✝) psi ↔ Holds D I V' M (head✝ :: tail✝) psi)
V V' : Valuation D
vs : List VarName
h2 : ∀ v ∈ vs, V v = V' v
h1_left : NoMetaVarAndAllFreeInList vs phi
h1_right : NoMetaVarAndAllFreeInList vs psi
a✝ : Holds D I V' M (head✝ :: tail✝) phi
⊢ Holds D I V M (head✝ :: tail✝) psi ↔ Holds D I V' M (head✝ :: tail✝) psi
no goals