have IHφ := repl_in_model_sat_iff x ψ φ M v
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w v : W
φ : Formula
⊢ relate M (repl_in_P x ψ (?'φ)) w v ↔ relate (repl_in_model x ψ M) (?'φ) w v
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w v : W
φ : Formula
IHφ : (M, v)⊨repl_in_F x ψ φ ↔ (repl_in_model x ψ M, v)⊨φ
⊢ relate M (repl_in_P x ψ (?'φ)) w v ↔ relate (repl_in_model x ψ M) (?'φ) w v