From 9ebf44d84754adc5b64fcf612c6816c02c80462d Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 2 Feb 2019 19:29:23 -0500
Subject: Imported Upstream version 8.9.0

---
 test-suite/ssr/absevarprop.v | 96 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 96 insertions(+)
 create mode 100644 test-suite/ssr/absevarprop.v

(limited to 'test-suite/ssr/absevarprop.v')

diff --git a/test-suite/ssr/absevarprop.v b/test-suite/ssr/absevarprop.v
new file mode 100644
index 00000000..fa1de009
--- /dev/null
+++ b/test-suite/ssr/absevarprop.v
@@ -0,0 +1,96 @@
+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
+
+Require Import ssreflect ssrbool ssrfun.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Lemma test15: forall (y : nat) (x : 'I_2), y < 1 -> val x = y -> Some x = insub y.
+move=> y x le_1 defx; rewrite insubT ?(leq_trans le_1) // => ?.
+by congr (Some _); apply: val_inj=> /=; exact: defx.
+Qed.
+
+Axiom P : nat -> Prop.
+Axiom Q : forall n, P n -> Prop.
+Definition R := fun (x : nat) (p : P x) m (q : P (x+1)) => m > 0.
+
+Inductive myEx : Type := ExI : forall n (pn : P n) pn', Q n pn -> R n pn n pn' -> myEx.
+
+Variable P1 : P 1.
+Variable P11 : P (1 + 1).
+Variable Q1 : forall P1, Q 1 P1.
+
+Lemma testmE1 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+  match goal with |- P 1 => exact: P1 | _ => fail end.
+  match goal with |- P (1+1) => exact: P11 | _ => fail end.
+  match goal with |- forall p : P 1, Q 1 p => move=> *; exact: Q1 | _ => fail end.
+match goal with |- forall (p : P 1) (q : P (1+1)), is_true (R 1 p 1 q) => done | _ => fail end.
+Qed.
+
+Lemma testE2 : exists y : { x | P x }, sval y = 1.
+Proof.
+apply: ex_intro (exist _ 1 _) _.
+  match goal with |- P 1 => exact: P1 | _ => fail end.
+match goal with |- forall p : P 1, @sval _ _ (@exist _ _ 1 p) = 1 => done | _ => fail end.
+Qed.
+
+Lemma testE3 : exists y : { x | P x }, sval y = 1.
+Proof.
+have := (ex_intro _ (exist _ 1 _) _); apply.
+  match goal with |- P 1 => exact: P1 | _ => fail end.
+match goal with |- forall p : P 1, @sval _ _ (@exist _ _ 1 p) = 1 => done | _ => fail end.
+Qed.
+
+Lemma testE4 : P 2 -> exists y : { x | P x }, sval y = 2.
+Proof.
+move=> P2; apply: ex_intro (exist _ 2 _) _.
+match goal with |- @sval _ _ (@exist _ _ 2 P2) = 2 => done | _ => fail end.
+Qed.
+
+Hint Resolve P1.
+
+Lemma testmE12 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+  match goal with |- P (1+1) => exact: P11 | _ => fail end.
+  match goal with |- Q 1 P1 => exact: Q1 | _ => fail end.
+match goal with |- forall (q : P (1+1)), is_true (R 1 P1 1 q) => done | _ => fail end.
+Qed.
+
+Create HintDb SSR.
+
+Hint Resolve P11 : SSR.
+
+Ltac ssrautoprop := trivial with SSR.
+
+Lemma testmE13 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+  match goal with |- Q 1 P1 => exact: Q1 | _ => fail end.
+match goal with |- is_true (R 1 P1 1 P11) => done | _ => fail end.
+Qed.
+
+Definition R1 := fun (x : nat) (p : P x) m (q : P (x+1)) (r : Q x p) => m > 0.
+
+Inductive myEx1 : Type :=
+  ExI1 : forall n (pn : P n) pn' (q : Q n pn), R1 n pn n pn' q -> myEx1.
+
+Hint Resolve (Q1 P1) : SSR.
+
+(* tests that goals in prop are solved in the right order, propagating instantiations,
+   thus the goal Q 1 ?p1 is faced by trivial after ?p1, and is thus evar free *)
+Lemma testmE14 : myEx1.
+Proof.
+apply: ExI1 1 _ _ _ _.
+match goal with |- is_true (R1 1 P1 1 P11 (Q1 P1)) => done | _ => fail end.
+Qed.
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