case star α =>
  have IHα := substitutionLemmaRel σ α M
  simp_all only [subst_in_P, relate]
  constructor
  all_goals
    apply Relation.ReflTransGen.mono
    intro w v
    rw [IHα w v]
    tauto
σ : Substitution
W : Type
M : KripkeModel W
w v : W
α : Program
⊢ relate M (subst_in_P σ (∗α)) w v ↔ relate (subst_in_model σ M) (∗α) w v
no goals