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/elim2.v | 74 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)
 create mode 100644 test-suite/ssr/elim2.v

(limited to 'test-suite/ssr/elim2.v')

diff --git a/test-suite/ssr/elim2.v b/test-suite/ssr/elim2.v
new file mode 100644
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--- /dev/null
+++ b/test-suite/ssr/elim2.v
@@ -0,0 +1,74 @@
+(************************************************************************)
+(*         *   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 ssrbool TestSuite.ssr_mini_mathcomp.
+(* div fintype finfun path bigop. *)
+
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Lemma big_load R (K K' : R -> Type) idx op I r (P : pred I) F :
+  let s := \big[op/idx]_(i <- r | P i) F i in
+  K s * K' s -> K' s.
+Proof. by move=> /= [_]. Qed.
+Arguments big_load [R] K [K' idx op I r P F].
+
+Section Elim1.
+
+Variables (R : Type) (K : R -> Type) (f : R -> R).
+Variables (idx : R) (op op' : R -> R -> R).
+
+Hypothesis Kid : K idx.
+
+Ltac ASSERT1 := match goal with |- (K idx) => myadmit end.
+Ltac ASSERT2 K := match goal with |- (forall x1 : R, R ->
+    forall y1 : R, R -> K x1 -> K y1 -> K (op x1 y1)) => myadmit end.
+
+
+Lemma big_rec I r (P : pred I) F
+    (Kop : forall i x, P i -> K x -> K (op (F i) x)) :
+  K (\big[op/idx]_(i <- r | P i) F i).
+Proof.
+elim/big_ind2: {-}_.
+  ASSERT1. ASSERT2 K. match goal with |- (forall i : I, is_true (P i) -> K (F i)) => myadmit end. Undo 4.
+elim/big_ind2: _ / {-}_.
+  ASSERT1. ASSERT2 K. match goal with |- (forall i : I, is_true (P i) -> K (F i)) => myadmit end. Undo 4.
+
+elim/big_rec2: (\big[op/idx]_(i <- r | P i) op idx (F i))
+  / (\big[op/idx]_(i <- r | P i) F i).
+  ASSERT1. match goal with |- (forall i : I, R -> forall y2 : R, is_true (P i) -> K y2 -> K (op (F i) y2)) => myadmit end. Undo 3.
+
+elim/(big_load (phantom R)): _.
+  Undo.
+
+Fail elim/big_rec2: {2}_.
+
+elim/big_rec2: (\big[op/idx]_(i <- r | P i) F i)
+  / {1}(\big[op/idx]_(i <- r | P i) F i).
+  Undo.
+
+elim/(big_load (phantom R)): _.
+Undo.
+
+Fail elim/big_rec2: _ / {2}(\big[op/idx]_(i <- r | P i) F i).
+Admitted.
+
+Definition morecomplexthannecessary A (P : A -> A -> Prop) x y := P x y.
+
+Lemma grab A (P : A -> A -> Prop) n m : (n = m) -> (P n n) -> morecomplexthannecessary A P n m.
+by move->.
+Qed.
+
+Goal forall n m, m + (n + m) = m + (n * 1 + m).
+Proof. move=> n m; elim/grab : (_ * _) / {1}n => //; exact: muln1. Qed.
+
+End Elim1.
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