have IHα := repl_in_model_rel_iff x ψ α M w
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w : W
α : Program
φ : Formula
⊢ (M, w)⊨repl_in_F x ψ (⌈α⌉φ) ↔ (repl_in_model x ψ M, w)⊨⌈α⌉φ
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w : W
α : Program
φ : Formula
IHα : ∀ (v : W), relate M (repl_in_P x ψ α) w v ↔ relate (repl_in_model x ψ M) α w v
⊢ (M, w)⊨repl_in_F x ψ (⌈α⌉φ) ↔ (repl_in_model x ψ M, w)⊨⌈α⌉φ