have IHα := repl_in_model_rel_iff x ψ α M
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w v : W
α β : Program
⊢ relate M (repl_in_P x ψ (α⋓β)) w v ↔ relate (repl_in_model x ψ M) (α⋓β) w v
x : ℕ
ψ : Formula
W : Type
M : KripkeModel W
w v : W
α β : Program
IHα : ∀ (w v : W), relate M (repl_in_P x ψ α) w v ↔ relate (repl_in_model x ψ M) α w v
⊢ relate M (repl_in_P x ψ (α⋓β)) w v ↔ relate (repl_in_model x ψ M) (α⋓β) w v