From bb6dc2355bcd027a3a89c40629b82eb2019eff6a Mon Sep 17 00:00:00 2001
From: Erik Martin-Dorel
Date: Mon, 4 Mar 2019 01:25:39 +0100
Subject: [ssr] under: Add iff support in side-conditions

---
 test-suite/ssr/under.v | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)

(limited to 'test-suite')

diff --git a/test-suite/ssr/under.v b/test-suite/ssr/under.v
index 5f27858d17..1e3b0f678b 100644
--- a/test-suite/ssr/under.v
+++ b/test-suite/ssr/under.v
@@ -162,3 +162,37 @@ under x: Lem.
 under Lem => [|x|] do [done|rewrite f_eq|done].
 done.
 Qed.
+
+
+(* Inspired From Coquelicot.Lub. *)
+(* http://coquelicot.saclay.inria.fr/html/Coquelicot.Lub.html#Lub_Rbar_eqset *)
+
+Parameters (R Rbar : Set) (R0 : R) (Rbar0 : Rbar).
+Parameter Rbar_le : Rbar -> Rbar -> Prop.
+Parameter Lub_Rbar : (R -> Prop) -> Rbar.
+Parameter Lub_Rbar_eqset :
+  forall E1 E2 : R -> Prop,
+    (forall x : R, E1 x <-> E2 x) ->
+    Lub_Rbar E1 = Lub_Rbar E2.
+
+Lemma test_Lub_Rbar (E : R -> Prop)  :
+  Rbar_le Rbar0 (Lub_Rbar (fun x => x = R0 \/ E x)).
+Proof.
+under Lub_Rbar_eqset => r.
+by rewrite over.
+Abort.
+
+
+Lemma ex_iff R (P1 P2 : R -> Prop) :
+  (forall x : R, P1 x <-> P2 x) -> ((exists x, P1 x) <-> (exists x, P2 x)).
+Proof.
+by move=> H; split; move=> [x Hx]; exists x; apply H.
+Qed.
+
+Arguments ex_iff [R P1] P2 iffP12.
+
+Require Import Setoid.
+Lemma test_ex_iff (P : nat -> Prop) : (exists x, P x) -> True.
+under ex_iff => n.
+by rewrite over.
+Abort.
-- 
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