Commit 717c38f4 authored by Robbert Krebbers's avatar Robbert Krebbers

Misc stuff about sigC.

parent 8d55728b
......@@ -1106,9 +1106,14 @@ Section sigma.
should not depend on A being an OFE. *)
Instance sig_equiv : Equiv (sig P) := λ x1 x2, `x1 `x2.
Instance sig_dist : Dist (sig P) := λ n x1 x2, `x1 {n} `x2.
Definition sig_equiv_alt x y : x y `x `y := reflexivity _.
Definition sig_dist_alt n x y : x {n} y `x {n} `y := reflexivity _.
Lemma exist_ne n a1 a2 (H1 : P a1) (H2 : P a2) :
a1 {n} a2 a1 H1 {n} a2 H2.
Proof. done. Qed.
Global Instance proj1_sig_ne : NonExpansive (@proj1_sig _ P).
Proof. by intros n [a Ha] [b Hb] ?. Qed.
Definition sig_ofe_mixin : OfeMixin (sig P).
......@@ -1126,13 +1131,8 @@ Section sigma.
intros ?? n c. apply (conv_compl n (chain_map proj1_sig c)).
Qed.
Global Instance sig_timeless (x : sig P) :
Timeless (proj1_sig x) Timeless x.
Proof.
intros ? [b ?]; destruct x as [a ?].
rewrite /dist /ofe_dist /= /sig_dist /equiv /ofe_equiv /= /sig_equiv /=.
apply (timeless _).
Qed.
Global Instance sig_timeless (x : sig P) : Timeless (`x) Timeless x.
Proof. intros ? y. rewrite sig_dist_alt sig_equiv_alt. apply (timeless _). Qed.
Global Instance sig_discrete_ofe : Discrete A Discrete sigC.
Proof. intros ??. apply _. Qed.
End sigma.
......
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