Commit 143fbc52 by Robbert Krebbers

### Prove that the dec_agree CMRA is total.

parent 59829441
 ... @@ -31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some. ... @@ -31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some. Definition dec_agree_ra_mixin : RAMixin (dec_agree A). Definition dec_agree_ra_mixin : RAMixin (dec_agree A). Proof. Proof. split. apply ra_total_mixin; apply _ || eauto. - apply _. - intros x y cx ? [=<-]; eauto. - apply _. - 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). - intros [?|] ? [=<-]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] [?|] ?? [=<-]; eauto. - by intros [?|] [?|] ?. - by intros [?|] [?|] ?. Qed. Qed. Canonical Structure dec_agreeR : cmraT := Canonical Structure dec_agreeR : cmraT := discreteR (dec_agree A) dec_agree_ra_mixin. discreteR (dec_agree A) dec_agree_ra_mixin. Global Instance dec_agree_total : CMRATotal dec_agreeR. Proof. intros x. by exists x. Qed. (* Some properties of this CMRA *) (* Some properties of this CMRA *) Global Instance dec_agree_persistent (x : dec_agreeR) : Persistent x. Global Instance dec_agree_persistent (x : dec_agreeR) : Persistent x. Proof. by constructor. Qed. Proof. by constructor. Qed. ... @@ -59,8 +57,10 @@ Proof. destruct x; by rewrite /= ?decide_True. Qed. ... @@ -59,8 +57,10 @@ Proof. destruct x; by rewrite /= ?decide_True. Qed. Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 = x2. Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 = x2. Proof. destruct x1, x2; by repeat (simplify_eq/= || case_match). Qed. Proof. destruct x1, x2; by repeat (simplify_eq/= || case_match). Qed. Lemma DecAgree_included a b : DecAgree a ≼ DecAgree b → a = b. Lemma DecAgree_included a b : DecAgree a ≼ DecAgree b ↔ a = b. Proof. intros [[c|] [=]%leibniz_equiv_iff]. by simplify_option_eq. Qed. Proof. split. intros [[c|] [=]%leibniz_equiv]. by simplify_option_eq. by intros ->. Qed. End dec_agree. End dec_agree. Arguments dec_agreeC : clear implicits. Arguments dec_agreeC : clear implicits. ... ...
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