diff --git a/algebra/upred.v b/algebra/upred.v index 472f6010d72b954ea4e3c8bdc06d0a4db2ddccf1..9258769d86d5fcdffae24cb7eecc65fbbb52fe71 100644 --- a/algebra/upred.v +++ b/algebra/upred.v @@ -750,17 +750,6 @@ Proof. apply and_intro; first by eauto. by rewrite {1}(later_intro P) later_impl impl_elim_r. Qed. -Lemma löb_all_1 {A} (Φ Ψ : A → uPred M) : - (∀ a, (▷ (∀ b, Φ b → Ψ b) ∧ Φ a) ⊑ Ψ a) → ∀ a, Φ a ⊑ Ψ a. -Proof. - intros Hlöb a. - (* Part I: Revert all the bits we need for the induction into the conclusion. *) - apply impl_entails. - rewrite -[(Φ a → Ψ a)%I](forall_elim (Ψ := λ a, Φ a → Ψ a)%I a). clear a. - (* Part II: Perform induction. *) - apply löb_strong, forall_intro=>a. apply impl_intro_r. - by rewrite left_id Hlöb. -Qed. (* Always *) Lemma always_const φ : (□ ■φ : uPred M)%I ≡ (■φ)%I.