exact
⟨fun h x => by simpa[Matrix.comp_vecCons''] using eval_ofEquiv_iff.mp (h (φ x)),
fun h x => eval_ofEquiv_iff.mpr (by simpa[Matrix.comp_vecCons''] using h (φ.symm x))⟩
M : Type u_2
N : Type u_1
L : Language
μ : Type v
μ₁ : Type v₁
μ₂ : Type v₂
s : Structure L M
φ : M ≃ N
x✝ : ℕ
e : Fin x✝ → N
ε : μ → N
p : Semiformula L μ (x✝ + 1)
⊢ (∀ (x : N), (Eval (ofEquiv φ) (x :> e) ε) p) ↔ ∀ (x : M), (Eval s (x :> ⇑φ.symm ∘ e) (⇑φ.symm ∘ ε)) p
no goals