Commit a50d23b9 authored by Robbert Krebbers's avatar Robbert Krebbers Committed by Ralf Jung

Omit spacing when pretty printing `N.@x` to reflect its tight precedence.

parent 274209c2
......@@ -19,7 +19,8 @@ Definition nclose_aux : { x | x = @nclose_def }. by eexists. Qed.
Instance nclose : UpClose namespace coPset := proj1_sig nclose_aux.
Definition nclose_eq : @nclose = @nclose_def := proj2_sig nclose_aux.
Infix ".@" := ndot (at level 19, left associativity) : C_scope.
Notation "N .@ x" := (ndot N x)
(at level 19, left associativity, format "N .@ x") : C_scope.
Notation "(.@)" := ndot (only parsing) : C_scope.
Instance ndisjoint : Disjoint namespace := λ N1 N2, nclose N1 nclose N2.
......@@ -41,7 +42,7 @@ Section namespace.
by apply elem_coPset_suffixes; exists xH; rewrite (left_id_L _ _).
Qed.
Lemma nclose_subseteq N x : N .@ x (N : coPset).
Lemma nclose_subseteq N x : N.@x (N : coPset).
Proof.
intros p; rewrite nclose_eq /nclose !ndot_eq !elem_coPset_suffixes.
intros [q ->]. destruct (list_encode_suffix N (ndot_def N x)) as [q' ?].
......@@ -49,25 +50,25 @@ Section namespace.
by exists (q ++ q')%positive; rewrite <-(assoc_L _); f_equal.
Qed.
Lemma nclose_subseteq' E N x : N E N .@ x E.
Lemma nclose_subseteq' E N x : N E N.@x E.
Proof. intros. etrans; eauto using nclose_subseteq. Qed.
Lemma ndot_nclose N x : encode (N .@ x) N.
Lemma ndot_nclose N x : encode (N.@x) N.
Proof. apply nclose_subseteq with x, encode_nclose. Qed.
Lemma nclose_infinite N : ¬set_finite ( N : coPset).
Proof. rewrite nclose_eq. apply coPset_suffixes_infinite. Qed.
Lemma ndot_ne_disjoint N x y : x y N .@ x N .@ y.
Lemma ndot_ne_disjoint N x y : x y N.@x N.@y.
Proof.
intros Hxy a. rewrite !nclose_eq !elem_coPset_suffixes !ndot_eq.
intros [qx ->] [qy Hqy].
revert Hqy. by intros [= ?%encode_inj]%list_encode_suffix_eq.
Qed.
Lemma ndot_preserve_disjoint_l N E x : N E N .@ x E.
Lemma ndot_preserve_disjoint_l N E x : N E N.@x E.
Proof. intros. pose proof (nclose_subseteq N x). set_solver. Qed.
Lemma ndot_preserve_disjoint_r N E x : E N E N .@ x.
Lemma ndot_preserve_disjoint_r N E x : E N E N.@x.
Proof. intros. by apply symmetry, ndot_preserve_disjoint_l. Qed.
Lemma ndisj_subseteq_difference N E F : E N E F E F N.
......
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