diff --git a/theories/bi/derived_laws.v b/theories/bi/derived_laws.v index 9229c6a02bcd5b6cf33671230626a210a6e33dad..8e99ebd7dbf99dc4f9aed534e10445fd9e3c1762 100644 --- a/theories/bi/derived_laws.v +++ b/theories/bi/derived_laws.v @@ -1934,6 +1934,16 @@ Proof. by rewrite plainly_pure True_impl. Qed. +Lemma plainly_True_alt P : bi_plainly (True -∗ P) ⊣⊢ P ≡ True. +Proof. + apply (anti_symm (⊢)). + - rewrite -prop_ext. apply plainly_mono, and_intro; apply wand_intro_l; auto. + by rewrite wand_elim_r. + - rewrite internal_eq_sym (internal_eq_rewrite _ _ + (λ Q, bi_plainly (True -∗ Q)) ltac:(solve_proper)). + by rewrite -entails_wand // -(plainly_emp_intro True%I) True_impl. +Qed. + Global Instance internal_eq_absorbing {A : ofeT} (x y : A) : Absorbing (x ≡ y : PROP)%I. Proof. by rewrite /Absorbing absorbingly_internal_eq. Qed.