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/gen_have.v | 174 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 174 insertions(+)
 create mode 100644 test-suite/ssr/gen_have.v

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

diff --git a/test-suite/ssr/gen_have.v b/test-suite/ssr/gen_have.v
new file mode 100644
index 00000000..249e006f
--- /dev/null
+++ b/test-suite/ssr/gen_have.v
@@ -0,0 +1,174 @@
+(************************************************************************)
+(*         *   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.
+Require Import ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Axiom P : nat -> Prop.
+Lemma clear_test (b1 b2 : bool) : b2 = b2.
+Proof.
+(* wlog gH : (b3 := b2) / b2 = b3. myadmit. *)
+gen have {b1} H, gH : (b3 := b2) (w := erefl 3) / b2 = b3.
+  myadmit.
+Fail exact (H b1).
+exact (H b2 (erefl _)).
+Qed.
+
+
+Lemma test1 n (ngt0 : 0 < n) : P n.
+gen have lt2le, /andP[H1 H2] : n ngt0 / (0 <= n) && (n != 0).
+  match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+Check (lt2le : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+Check (H1 : 0 <= n).
+Check (H2 : n != 0).
+myadmit.
+Qed.
+
+Lemma test2 n (ngt0 : 0 < n) : P n.
+gen have _, /andP[H1 H2] : n ngt0 / (0 <= n) && (n != 0).
+  match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+lazymatch goal with
+ | lt2le : forall n : nat, is_true(0 < n) -> is_true((0 <= n) && (n != 0))
+    |- _ => fail "not cleared"
+ | _ => idtac end.
+Check (H1 : 0 <= n).
+Check (H2 : n != 0).
+myadmit.
+Qed.
+
+Lemma test3 n (ngt0 : 0 < n) : P n.
+gen have H : n ngt0 / (0 <= n) && (n != 0).
+  match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+Check (H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test4 n (ngt0 : 0 < n) : P n.
+gen have : n ngt0 / (0 <= n) && (n != 0).
+  match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+move=> H.
+Check(H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test4bis n (ngt0 : 0 < n) : P n.
+wlog suff : n ngt0 / (0 <= n) && (n != 0); last first.
+  match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+move=> H.
+Check(H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test5 n (ngt0 : 0 < n) : P n.
+Fail gen have : / (0 <= n) && (n != 0).
+Abort.
+
+Lemma test6 n (ngt0 : 0 < n) : P n.
+gen have : n ngt0 / (0 <= n) && (n != 0) by myadmit.
+Abort.
+
+Lemma test7 n (ngt0 : 0 < n) : P n.
+Fail gen have : n / (0 <= n) && (n != 0).
+Abort.
+
+Lemma test3wlog2 n (ngt0 : 0 < n) : P n.
+gen have H : (m := n) ngt0 / (0 <= m) && (m != 0).
+  match goal with
+    ngt0 : is_true(0 < m) |- is_true((0 <= m) && (m != 0)) => myadmit end.
+Check (H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test3wlog3 n (ngt0 : 0 < n) : P n.
+gen have H : {n} (m := n) (n := 0) ngt0 / (0 <= m) && (m != n).
+  match goal with
+    ngt0 : is_true(n < m) |- is_true((0 <= m) && (m != n)) => myadmit end.
+Check (H : forall m n : nat, n < m -> (0 <= m) && (m != n)).
+myadmit.
+Qed.
+
+Lemma testw1 n (ngt0 : 0 < n) : n <= 0.
+wlog H : (z := 0) (m := n) ngt0 / m != 0.
+  match goal with
+    |- (forall z m,
+          is_true(z < m) -> is_true(m != 0) -> is_true(m <= z)) ->
+       is_true(n <= 0) => myadmit end.
+Check(n : nat).
+Check(m : nat).
+Check(z : nat).
+Check(ngt0 : z < m).
+Check(H : m != 0).
+myadmit.
+Qed.
+
+Lemma testw2 n (ngt0 : 0 < n) : n <= 0.
+wlog H : (m := n) (z := (X in n <= X)) ngt0 / m != z.
+  match goal with
+    |- (forall m z : nat,
+          is_true(0 < m) -> is_true(m != z) -> is_true(m <= z)) ->
+            is_true(n <= 0)   => idtac end.
+Restart.
+wlog H : (m := n) (one := (X in X <= _)) ngt0 / m != one.
+  match goal with
+    |- (forall m one : nat,
+          is_true(one <= m) -> is_true(m != one) -> is_true(m <= 0)) ->
+            is_true(n <= 0)   => idtac end.
+Restart.
+wlog H : {n} (m := n) (z := (X in _ <= X)) ngt0 / m != z.
+  match goal with
+    |- (forall m z : nat,
+          is_true(0 < z) -> is_true(m != z) -> is_true(m <= 0)) ->
+            is_true(n <= 0)   => idtac end.
+  myadmit.
+Fail Check n.
+myadmit.
+Qed.
+
+Section Test.
+Variable x : nat.
+Definition addx y := y + x.
+
+Lemma testw3 (m n : nat) (ngt0 : 0 < n) : n <= addx x.
+wlog H : (n0 := n) (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
+  myadmit.
+myadmit.
+Qed.
+
+
+Definition twox := x + x.
+Definition bis := twox.
+
+Lemma testw3x n (ngt0 : 0 < n) : n + x <= twox.
+wlog H : (y := x) (@twoy := (X in _ <= X)) / twoy = 2 * y.
+  match goal with
+    |- (forall y : nat,
+         let twoy := y + y in
+         twoy = 2 * y -> is_true(n + y <= twoy)) ->
+       is_true(n + x <= twox) => myadmit end.
+Restart.
+wlog H : (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
+  match goal with
+    |- (forall y : nat,
+         let twoy := twox in
+         twoy = 2 * y -> is_true(n + y <= twoy)) ->
+       is_true(n + x <= twox) => myadmit end.
+myadmit.
+Qed.
+
+End Test.
+
+Lemma test_in n k (def_k : k = 0) (ngtk : k < n) : P n.
+rewrite -(add0n n) in {def_k k ngtk} (m := k) (def_m := def_k) (ngtm := ngtk).
+rewrite def_m add0n in {ngtm} (e := erefl 0 ) (ngt0 := ngtm) => {def_m}.
+myadmit.
+Qed.
-- 
cgit v1.2.3