Commit 05817be7 authored by Ralf Jung's avatar Ralf Jung
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show that we can rewrite below a contractive function even if we have an equality only later

parent b2a210fe
...@@ -497,10 +497,11 @@ Proof. unseal; intros HΦΨ; split=> n x ? [a ?]; by apply HΦΨ with a. Qed. ...@@ -497,10 +497,11 @@ Proof. unseal; intros HΦΨ; split=> n x ? [a ?]; by apply HΦΨ with a. Qed.
Lemma eq_refl {A : cofeT} (a : A) : True (a a). Lemma eq_refl {A : cofeT} (a : A) : True (a a).
Proof. unseal; by split=> n x ??; simpl. Qed. Proof. unseal; by split=> n x ??; simpl. Qed.
Lemma eq_rewrite {A : cofeT} a b (Ψ : A uPred M) P Lemma eq_rewrite {A : cofeT} a b (Ψ : A uPred M) P
`{HΨ : n, Proper (dist n ==> dist n) Ψ} : P (a b) P Ψ a P Ψ b. {HΨ : n, Proper (dist n ==> dist n) Ψ} : P (a b) P Ψ a P Ψ b.
Proof. Proof.
unseal; intros Hab Ha; split=> n x ??. unseal; intros Hab Ha; split=> n x ??. apply HΨ with n a; auto.
apply HΨ with n a; auto. by symmetry; apply Hab with x. by apply Ha. - by symmetry; apply Hab with x.
- by apply Ha.
Qed. Qed.
Lemma eq_equiv `{Empty M, !CMRAUnit M} {A : cofeT} (a b : A) : Lemma eq_equiv `{Empty M, !CMRAUnit M} {A : cofeT} (a b : A) :
True (a b) a b. True (a b) a b.
...@@ -508,6 +509,14 @@ Proof. ...@@ -508,6 +509,14 @@ Proof.
unseal=> Hab; apply equiv_dist; intros n; apply Hab with ; last done. unseal=> Hab; apply equiv_dist; intros n; apply Hab with ; last done.
apply cmra_valid_validN, cmra_unit_valid. apply cmra_valid_validN, cmra_unit_valid.
Qed. Qed.
Lemma eq_rewrite_contractive {A : cofeT} a b (Ψ : A uPred M) P
{HΨ : Contractive Ψ} : P (a b) P Ψ a P Ψ b.
Proof.
unseal; intros Hab Ha; split=> n x ??. apply HΨ with n a; auto.
- destruct n; intros m ?; first omega. apply (dist_le n); last omega.
symmetry. by destruct Hab as [Hab]; eapply (Hab (S n)).
- by apply Ha.
Qed.
(* Derived logical stuff *) (* Derived logical stuff *)
Lemma False_elim P : False P. Lemma False_elim P : False P.
......
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