(* Copyright 2010 IMDEA Software Institute Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *)
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(* This file is Prelude -- often used notation definitions and lemmas that    *)
(* are not included in the other libraries.                                   *)
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Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
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(* Prelude *)
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(* export inj_pair without exporting the whole Eqdep library *)
Definition inj_pair2 := @inj_pair2.
Arguments inj_pair2 [U P p x y] _.
Prenex Implicits inj_pair2.
(* eta laws for pairs and units *)
Notation prod_eta := surjective_pairing.

(* Specifications: *)
(* eta law often used with injection *)
Lemma prod_inj A B (x y : A * B) : x = y <-> (x.1, x.2) = (y.1, y.2).
Lemma and7P : reflect [/\ b1, b2, b3, b4, b5, b6 & b7]
[&& b1, b2, b3, b4, b5, b6 & b7].
Lemma or5P : reflect [\/ b1, b2, b3, b4 | b5] [|| b1, b2, b3, b4 | b5].
Lemma or6P : reflect [\/ b1, b2, b3, b4, b5 | b6] [|| b1, b2, b3, b4, b5 | b6].
Lemma or7P : reflect [\/ b1, b2, b3, b4, b5, b6 | b7]
[|| b1, b2, b3, b4, b5, b6 | b7].