Commit 5061c3cb authored by Robbert Krebbers's avatar Robbert Krebbers

Rename preserving -> mono.

To be consistent with Iris, see Iris commit 9ee62b3a.
parent 81d719c9
...@@ -346,11 +346,11 @@ Section simple_collection. ...@@ -346,11 +346,11 @@ Section simple_collection.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma elem_of_union_r x X Y : x Y x X Y. Lemma elem_of_union_r x X Y : x Y x X Y.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma union_preserving_l X Y1 Y2 : Y1 Y2 X Y1 X Y2. Lemma union_mono_l X Y1 Y2 : Y1 Y2 X Y1 X Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma union_preserving_r X1 X2 Y : X1 X2 X1 Y X2 Y. Lemma union_mono_r X1 X2 Y : X1 X2 X1 Y X2 Y.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma union_preserving X1 X2 Y1 Y2 : X1 X2 Y1 Y2 X1 Y1 X2 Y2. Lemma union_mono X1 X2 Y1 Y2 : X1 X2 Y1 Y2 X1 Y1 X2 Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Global Instance union_idemp : IdemP (() : relation C) (). Global Instance union_idemp : IdemP (() : relation C) ().
...@@ -444,8 +444,8 @@ Section simple_collection. ...@@ -444,8 +444,8 @@ Section simple_collection.
by rewrite reverse_cons, union_list_app, by rewrite reverse_cons, union_list_app,
union_list_singleton, (comm _), IH. union_list_singleton, (comm _), IH.
Qed. Qed.
Lemma union_list_preserving Xs Ys : Xs * Ys Xs Ys. Lemma union_list_mono Xs Ys : Xs * Ys Xs Ys.
Proof. induction 1; simpl; auto using union_preserving. Qed. Proof. induction 1; simpl; auto using union_mono. Qed.
Lemma empty_union_list Xs : Xs Forall ( ) Xs. Lemma empty_union_list Xs : Xs Forall ( ) Xs.
Proof. Proof.
split. split.
...@@ -565,11 +565,11 @@ Section collection. ...@@ -565,11 +565,11 @@ Section collection.
Lemma intersection_greatest X Y Z : Z X Z Y Z X Y. Lemma intersection_greatest X Y Z : Z X Z Y Z X Y.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma intersection_preserving_l X Y1 Y2 : Y1 Y2 X Y1 X Y2. Lemma intersection_mono_l X Y1 Y2 : Y1 Y2 X Y1 X Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma intersection_preserving_r X1 X2 Y : X1 X2 X1 Y X2 Y. Lemma intersection_mono_r X1 X2 Y : X1 X2 X1 Y X2 Y.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma intersection_preserving X1 X2 Y1 Y2 : Lemma intersection_mono X1 X2 Y1 Y2 :
X1 X2 Y1 Y2 X1 Y1 X2 Y2. X1 X2 Y1 Y2 X1 Y1 X2 Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
...@@ -612,12 +612,12 @@ Section collection. ...@@ -612,12 +612,12 @@ Section collection.
Lemma difference_disjoint X Y : X Y X Y X. Lemma difference_disjoint X Y : X Y X Y X.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma difference_preserving X1 X2 Y1 Y2 : Lemma difference_mono X1 X2 Y1 Y2 :
X1 X2 Y2 Y1 X1 Y1 X2 Y2. X1 X2 Y2 Y1 X1 Y1 X2 Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma difference_preserving_l X Y1 Y2 : Y2 Y1 X Y1 X Y2. Lemma difference_mono_l X Y1 Y2 : Y2 Y1 X Y1 X Y2.
Proof. set_solver. Qed. Proof. set_solver. Qed.
Lemma difference_preserving_r X1 X2 Y : X1 X2 X1 Y X2 Y. Lemma difference_mono_r X1 X2 Y : X1 X2 X1 Y X2 Y.
Proof. set_solver. Qed. Proof. set_solver. Qed.
(** Disjointness *) (** Disjointness *)
......
...@@ -1322,17 +1322,17 @@ Proof. intros. trans m2; auto using map_union_subseteq_l. Qed. ...@@ -1322,17 +1322,17 @@ Proof. intros. trans m2; auto using map_union_subseteq_l. Qed.
Lemma map_union_subseteq_r_alt {A} (m1 m2 m3 : M A) : Lemma map_union_subseteq_r_alt {A} (m1 m2 m3 : M A) :
m2 m3 m1 m3 m1 m2 m3. m2 m3 m1 m3 m1 m2 m3.
Proof. intros. trans m3; auto using map_union_subseteq_r. Qed. Proof. intros. trans m3; auto using map_union_subseteq_r. Qed.
Lemma map_union_preserving_l {A} (m1 m2 m3 : M A) : m1 m2 m3 m1 m3 m2. Lemma map_union_mono_l {A} (m1 m2 m3 : M A) : m1 m2 m3 m1 m3 m2.
Proof. Proof.
rewrite !map_subseteq_spec. intros ???. rewrite !map_subseteq_spec. intros ???.
rewrite !lookup_union_Some_raw. naive_solver. rewrite !lookup_union_Some_raw. naive_solver.
Qed. Qed.
Lemma map_union_preserving_r {A} (m1 m2 m3 : M A) : Lemma map_union_mono_r {A} (m1 m2 m3 : M A) :
m2 m3 m1 m2 m1 m3 m2 m3. m2 m3 m1 m2 m1 m3 m2 m3.
Proof. Proof.
intros. rewrite !(map_union_comm _ m3) intros. rewrite !(map_union_comm _ m3)
by eauto using map_disjoint_weaken_l. by eauto using map_disjoint_weaken_l.
by apply map_union_preserving_l. by apply map_union_mono_l.
Qed. Qed.
Lemma map_union_reflecting_l {A} (m1 m2 m3 : M A) : Lemma map_union_reflecting_l {A} (m1 m2 m3 : M A) :
m3 m1 m3 m2 m3 m1 m3 m2 m1 m2. m3 m1 m3 m2 m3 m1 m3 m2 m1 m2.
......
...@@ -288,12 +288,12 @@ Lemma gmultiset_union_subseteq_l X Y : X ⊆ X ∪ Y. ...@@ -288,12 +288,12 @@ Lemma gmultiset_union_subseteq_l X Y : X ⊆ X ∪ Y.
Proof. intros x. rewrite multiplicity_union. omega. Qed. Proof. intros x. rewrite multiplicity_union. omega. Qed.
Lemma gmultiset_union_subseteq_r X Y : Y X Y. Lemma gmultiset_union_subseteq_r X Y : Y X Y.
Proof. intros x. rewrite multiplicity_union. omega. Qed. Proof. intros x. rewrite multiplicity_union. omega. Qed.
Lemma gmultiset_union_preserving X1 X2 Y1 Y2 : X1 X2 Y1 Y2 X1 Y1 X2 Y2. Lemma gmultiset_union_mono X1 X2 Y1 Y2 : X1 X2 Y1 Y2 X1 Y1 X2 Y2.
Proof. intros ?? x. rewrite !multiplicity_union. by apply Nat.add_le_mono. Qed. Proof. intros ?? x. rewrite !multiplicity_union. by apply Nat.add_le_mono. Qed.
Lemma gmultiset_union_preserving_l X Y1 Y2 : Y1 Y2 X Y1 X Y2. Lemma gmultiset_union_mono_l X Y1 Y2 : Y1 Y2 X Y1 X Y2.
Proof. intros. by apply gmultiset_union_preserving. Qed. Proof. intros. by apply gmultiset_union_mono. Qed.
Lemma gmultiset_union_preserving_r X1 X2 Y : X1 X2 X1 Y X2 Y. Lemma gmultiset_union_mono_r X1 X2 Y : X1 X2 X1 Y X2 Y.
Proof. intros. by apply gmultiset_union_preserving. Qed. Proof. intros. by apply gmultiset_union_mono. Qed.
Lemma gmultiset_subset X Y : X Y size X < size Y X Y. Lemma gmultiset_subset X Y : X Y size X < size Y X Y.
Proof. intros. apply strict_spec_alt; split; naive_solver auto with omega. Qed. Proof. intros. apply strict_spec_alt; split; naive_solver auto with omega. Qed.
......
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