Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

algebra/cmra.v

@@ -272,8 +272,12 @@ Lemma cmra_unit_preserving x y : x ≼ y → unit x ≼ unit y.
 Proof. rewrite !cmra_included_includedN; eauto using cmra_unit_preservingN. Qed.
 Lemma cmra_included_unit x : unit x ≼ x.
 Proof. by exists x; rewrite cmra_unit_l. Qed.
+Lemma cmra_preservingN_l n x y z : x ≼{n} y → z ⋅ x ≼{n} z ⋅ y.
+Proof. by intros [z1 Hz1]; exists z1; rewrite Hz1 (associative op). Qed.
 Lemma cmra_preserving_l x y z : x ≼ y → z ⋅ x ≼ z ⋅ y.
 Proof. by intros [z1 Hz1]; exists z1; rewrite Hz1 (associative op). Qed.
+Lemma cmra_preservingN_r n x y z : x ≼{n} y → x ⋅ z ≼{n} y ⋅ z.
+Proof. by intros; rewrite -!(commutative _ z); apply cmra_preservingN_l. Qed.
 Lemma cmra_preserving_r x y z : x ≼ y → x ⋅ z ≼ y ⋅ z.
 Proof. by intros; rewrite -!(commutative _ z); apply cmra_preserving_l. Qed.
 

prelude/numbers.v

@@ -28,10 +28,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%nat : nat_
 Notation "(≤)" := le (only parsing) : nat_scope.
 Notation "(<)" := lt (only parsing) : nat_scope.
 
-Infix "≥" := ge : nat_scope.
-Notation "(≥)" := ge (only parsing) : nat_scope.
-Notation "(>)" := gt (only parsing) : nat_scope.
-
 Infix "`div`" := Nat.div (at level 35) : nat_scope.
 Infix "`mod`" := Nat.modulo (at level 35) : nat_scope.
 
@@ -108,10 +104,6 @@ Notation "(<)" := Pos.lt (only parsing) : positive_scope.
 Notation "(~0)" := xO (only parsing) : positive_scope.
 Notation "(~1)" := xI (only parsing) : positive_scope.
 
-Infix "≥" := Pos.ge : positive_scope.
-Notation "(≥)" := Pos.ge (only parsing) : positive_scope.
-Notation "(>)" := Pos.gt (only parsing) : positive_scope.
-
 Arguments Pos.of_nat _ : simpl never.
 Instance positive_eq_dec: ∀ x y : positive, Decision (x = y) := Pos.eq_dec.
 Instance positive_inhabited: Inhabited positive := populate 1.
@@ -187,11 +179,6 @@ Notation "x < y ≤ z" := (x < y ∧ y ≤ z)%N : N_scope.
 Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%N : N_scope.
 Notation "(≤)" := N.le (only parsing) : N_scope.
 Notation "(<)" := N.lt (only parsing) : N_scope.
-
-Infix "≥" := N.ge : N_scope.
-Notation "(≥)" := N.ge (only parsing) : N_scope.
-Notation "(>)" := N.gt (only parsing) : N_scope.
-
 Infix "`div`" := N.div (at level 35) : N_scope.
 Infix "`mod`" := N.modulo (at level 35) : N_scope.
 
@@ -226,10 +213,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Z_scope.
 Notation "(≤)" := Z.le (only parsing) : Z_scope.
 Notation "(<)" := Z.lt (only parsing) : Z_scope.
 
-Infix "≥" := Z.ge : Z_scope.
-Notation "(≥)" := Z.ge (only parsing) : Z_scope.
-Notation "(>)" := Z.gt (only parsing) : Z_scope.
-
 Infix "`div`" := Z.div (at level 35) : Z_scope.
 Infix "`mod`" := Z.modulo (at level 35) : Z_scope.
 Infix "`quot`" := Z.quot (at level 35) : Z_scope.
@@ -345,10 +328,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Qc_scope
 Notation "(≤)" := Qcle (only parsing) : Qc_scope.
 Notation "(<)" := Qclt (only parsing) : Qc_scope.
 
-Infix "≥" := Qcge : Qc_scope.
-Notation "(≥)" := Qcge (only parsing) : Qc_scope.
-Notation "(>)" := Qcgt (only parsing) : Qc_scope.
-
 Hint Extern 1 (_ ≤ _) => reflexivity || discriminate.
 Arguments Qred _ : simpl never.