Commit 91c5bb27 by Robbert Krebbers

### More Propers about logic.

parent 4e7a56c1
 ... ... @@ -43,13 +43,22 @@ Proof. by intros x1 x2 Hx; apply iprop_holds_ne, equiv_dist. Qed. Definition iPropC (A : cmraT) : cofeT := CofeT (iProp A). (** functor *) Program Definition iProp_map {A B : cmraT} (f: B -n> A) `{!CMRAPreserving f} Program Definition iprop_map {A B : cmraT} (f : B → A) `{!∀ n, Proper (dist n ==> dist n) f, !CMRAPreserving f} (P : iProp A) : iProp B := {| iprop_holds n x := P n (f x) |}. Next Obligation. by intros A B f ? P y1 y2 n ? Hy; simpl; rewrite <-Hy. Qed. Next Obligation. by intros A B f ?? P y1 y2 n ? Hy; simpl; rewrite <-Hy. Qed. Next Obligation. by intros A B f ? P y1 y2 n i ???; simpl; apply iprop_weaken; auto; by intros A B f ?? P y1 y2 n i ???; simpl; apply iprop_weaken; auto; apply validN_preserving || apply included_preserving. Qed. Instance iprop_map_ne {A B : cmraT} (f : B → A) `{!∀ n, Proper (dist n ==> dist n) f, !CMRAPreserving f} : Proper (dist n ==> dist n) (iprop_map f). Proof. by intros n x1 x2 Hx y n'; split; apply Hx; try apply validN_preserving. Qed. Definition ipropC_map {A B : cmraT} (f : B -n> A) `{!CMRAPreserving f} : iPropC A -n> iPropC B := CofeMor (iprop_map f : iPropC A → iPropC B). (** logical entailement *) Instance iprop_entails {A} : SubsetEq (iProp A) := λ P Q, ∀ x n, ... ... @@ -249,6 +258,24 @@ Global Instance iprop_exist_proper {B : cofeT} : Proof. by intros P1 P2 HP12 x n'; split; intros [a HP]; exists a; apply HP12. Qed. Global Instance iprop_later_contractive : Contractive (@iprop_later A). Proof. intros n P Q HPQ x [|n'] ??; simpl; [done|]. apply HPQ; eauto using cmra_valid_S. Qed. Global Instance iprop_later_proper : Proper ((≡) ==> (≡)) (@iprop_later A) := ne_proper _. Global Instance iprop_always_ne n: Proper (dist n ==> dist n) (@iprop_always A). Proof. intros P1 P2 HP x n'; split; apply HP; eauto using cmra_unit_valid. Qed. Global Instance iprop_always_proper : Proper ((≡) ==> (≡)) (@iprop_always A) := ne_proper _. Global Instance iprop_own_ne n : Proper (dist n ==> dist n) (@iprop_own A). Proof. by intros a1 a2 Ha x n'; split; intros [a' ?]; exists a'; simpl; first [rewrite <-(dist_le _ _ _ _ Ha) by lia|rewrite (dist_le _ _ _ _ Ha) by lia]. Qed. Global Instance iprop_own_proper : Proper ((≡) ==> (≡)) (@iprop_own A) := ne_proper _. (** Introduction and elimination rules *) Lemma iprop_True_intro P : P ⊆ True%I. ... ... @@ -339,11 +366,6 @@ Lemma iprop_sep_forall `(P : B → iProp A) Q : Proof. by intros x n ? (x1&x2&Hx&?&?); intros b; exists x1, x2. Qed. (* Later *) Global Instance iprop_later_contractive : Contractive (@iprop_later A). Proof. intros n P Q HPQ x [|n'] ??; simpl; [done|]. apply HPQ; eauto using cmra_valid_S. Qed. Lemma iprop_later_weaken P : P ⊆ (▷ P)%I. Proof. intros x [|n] ??; simpl in *; [done|]. ... ...
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