have IHα := substitutionLemmaRel σ α M
σ : Substitution
W : Type
M : KripkeModel W
w v : W
α β : Program
⊢ relate M (subst_in_P σ (α⋓β)) w v ↔ relate (subst_in_model σ M) (α⋓β) w v
σ : Substitution
W : Type
M : KripkeModel W
w v : W
α β : Program
IHα : ∀ (w v : W), relate M (subst_in_P σ α) w v ↔ relate (subst_in_model σ M) α w v
⊢ relate M (subst_in_P σ (α⋓β)) w v ↔ relate (subst_in_model σ M) (α⋓β) w v