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Diffstat (limited to 'test-suite/ssr/elim2.v')
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diff --git a/test-suite/ssr/elim2.v b/test-suite/ssr/elim2.v new file mode 100644 index 00000000..c7c20d8f --- /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. |