Commit 1d3902ca authored by Robbert Krebbers's avatar Robbert Krebbers

Misc tweaks.

parent 86967a81
......@@ -991,28 +991,25 @@ End limit_preserving.
Section sigma.
Context {A : ofeT} {P : A Prop}.
Implicit Types x : sig P.
(* TODO: Find a better place for this Equiv instance. It also
should not depend on A being an OFE. *)
Instance sig_equiv : Equiv (sig P) :=
λ x1 x2, (proj1_sig x1) (proj1_sig x2).
Instance sig_dist : Dist (sig P) :=
λ n x1 x2, (proj1_sig x1) {n} (proj1_sig x2).
Lemma exist_ne :
n x1 x2, x1 {n} x2
(H1 : P x1) (H2 : P x2), (exist P x1 H1) {n} (exist P x2 H2).
Proof. intros n ?? Hx ??. exact Hx. Qed.
Instance sig_equiv : Equiv (sig P) := λ x1 x2, `x1 `x2.
Instance sig_dist : Dist (sig P) := λ n x1 x2, `x1 {n} `x2.
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 : Proper (dist n ==> dist n) (@proj1_sig _ P).
Proof. intros n [] [] ?. done. Qed.
Proof. by intros n [a Ha] [b Hb] ?. Qed.
Definition sig_ofe_mixin : OfeMixin (sig P).
Proof.
split.
- intros x y. unfold dist, sig_dist, equiv, sig_equiv.
destruct x, y. apply equiv_dist.
- unfold dist, sig_dist. intros n.
split; [intros [] | intros [] [] | intros [] [] []]; simpl; try done.
intros. by etrans.
- intros n [??] [??]. unfold dist, sig_dist. simpl. apply dist_S.
- intros [a ?] [b ?]. rewrite /dist /sig_dist /equiv /sig_equiv /=.
apply equiv_dist.
- intros n. rewrite /dist /sig_dist.
split; [intros []| intros [] []| intros [] [] []]=> //= -> //.
- intros n [a ?] [b ?]. rewrite /dist /sig_dist /=. apply dist_S.
Qed.
Canonical Structure sigC : ofeT := OfeT (sig P) sig_ofe_mixin.
......@@ -1020,13 +1017,11 @@ Section sigma.
suddenly becomes explicit...? *)
Program Definition sig_compl `{LimitPreserving _ P} : Compl sigC :=
λ c, exist P (compl (chain_map proj1_sig c)) _.
Next Obligation.
intros ? Hlim c. apply Hlim. move=>n /=. destruct (c n). done.
Qed.
Program Definition sig_cofe `{LimitPreserving _ P} : Cofe sigC :=
Next Obligation. intros ? Hlim c. apply Hlim=> n /=. by destruct (c n). Qed.
Program Definition sig_cofe `{Cofe A, !LimitPreserving P} : Cofe sigC :=
{| compl := sig_compl |}.
Next Obligation.
intros ? Hlim n c. apply (conv_compl n (chain_map proj1_sig c)).
intros ?? n c. apply (conv_compl n (chain_map proj1_sig c)).
Qed.
Global Instance sig_timeless (x : sig P) :
......
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