Commit fd2acffe authored by Ralf Jung's avatar Ralf Jung

show an alternative characterization of plainly

parent 60c28208
......@@ -978,6 +978,17 @@ Lemma plainly_plainly P `{!Plain P} : ■ P ⊣⊢ P.
Proof. apply (anti_symm ()); eauto. Qed.
Lemma plainly_intro P Q `{!Plain P} : (P Q) P Q.
Proof. rewrite -(plainly_plainly P); apply plainly_intro'. Qed.
Lemma plainly_alt P : P P True.
apply (anti_symm ()).
- rewrite -prop_ext. apply plainly_intro'. rewrite plainly_elim.
apply and_intro; apply impl_intro_r.
+ apply True_intro.
+ apply and_elim_l.
- rewrite internal_eq_sym (internal_eq_rewrite _ _ (λ P, P)%I).
eapply impl_elim; first reflexivity.
rewrite plainly_pure. apply True_intro.
Lemma bupd_plain P `{!Plain P} : (|==> P) P.
Proof. by rewrite -{1}(plainly_plainly P) bupd_plainly. Qed.
......@@ -650,7 +650,7 @@ Proof.
- intros i a b; eapply Hf, ucmra_unit_validN.
(* Functions *)
(* Function extensionality *)
Lemma ofe_funC_equivI {A B} (f g : A -c> B) : f g x, f x g x.
Proof. by unseal. Qed.
Lemma ofe_morC_equivI {A B : ofeT} (f g : A -n> B) : f g x, f x g x.
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