Commit d4a687a8 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove (■ φ → P) ⊣⊢ (∀ _ : φ, P).

parent 588b9559
......@@ -265,6 +265,12 @@ Proof. by intros ->. Qed.
Lemma internal_eq_sym {A : cofeT} (a b : A) : a b b a.
Proof. apply (internal_eq_rewrite a b (λ b, b a)%I); auto. solve_proper. Qed.
Lemma pure_impl_forall φ P : ( φ P) ( _ : φ, P).
Proof.
apply (anti_symm _).
- apply forall_intro=> ?. by rewrite pure_equiv // left_id.
- apply impl_intro_l, pure_elim_l=> Hφ. by rewrite (forall_elim Hφ).
Qed.
Lemma pure_alt φ : φ _ : φ, True.
Proof.
apply (anti_symm _).
......
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