Commit 4f1ed7c9 by Robbert Krebbers

Clean up dec_agree.

```Most notably, there is no need to internalize stuff into the logic
as it follows from generic lemmas for discrete COFEs/CMRAs.```
parent eb8dd726
 From algebra Require Export cmra. From algebra Require Import functor upred. Local Arguments validN _ _ _ !_ /. Local Arguments valid _ _ !_ /. Local Arguments op _ _ _ !_ /. Local Arguments unit _ _ !_ /. (* This is isomorphic to optiob, but has a very different RA structure. *) (* This is isomorphic to option, but has a very different RA structure. *) Inductive dec_agree (A : Type) : Type := | DecAgree : A → dec_agree A | DecAgreeBot : dec_agree A. ... ... @@ -35,33 +34,23 @@ Proof. - apply _. - apply _. - apply _. - intros [?|] [?|] [?|]; simpl; repeat (case_match; simpl); subst; congruence. - intros [?|] [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|] [?|] ?; simpl; done. - intros [?|] [?|] ?; simpl; done. - intros [?|] [?|] [[?|]]; simpl; repeat (case_match; simpl); subst; try congruence; []. case=>EQ. destruct EQ. done. - intros [?|] [?|] [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] [?|]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - by intros [?|] [?|] ?. - by intros [?|] [?|] ?. - intros [?|] [?|] [[?|]]; fold_leibniz; intros; by repeat (simplify_eq/= || case_match). Qed. Canonical Structure dec_agreeRA : cmraT := discreteRA dec_agree_ra. (* Some properties of this CMRA *) Lemma dec_agree_idemp (x : dec_agree A) : x ⋅ x ≡ x. Proof. destruct x as [x|]; simpl; repeat (case_match; simpl); try subst; congruence. Qed. Proof. destruct x; by repeat (simplify_eq/= || case_match). Qed. Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 ≡ x2. Proof. destruct x1 as [x1|], x2 as [x2|]; simpl;repeat (case_match; simpl); by subst. Qed. Lemma dec_agree_equivI {M} a b : (DecAgree a ≡ DecAgree b)%I ≡ (a = b : uPred M)%I. Proof. do 2 split. by case. by destruct 1. Qed. Lemma dec_agree_validI {M} (x y : dec_agreeRA) : ✓ (x ⋅ y) ⊑ (x = y : uPred M). Proof. split=> r n _ ?. by apply: dec_agree_op_inv. Qed. Proof. destruct x1, x2; by repeat (simplify_eq/= || case_match). Qed. End dec_agree.
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