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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \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) *)
(************************************************************************)
(** Utilities for SProp users. *)
Set Universe Polymorphism.
Set Polymorphic Inductive Cumulativity.
Record Box (A:SProp) : Prop := box { unbox : A }.
Arguments box {_} _.
Arguments unbox {_} _.
Inductive Squash (A:Type) : SProp := squash : A -> Squash A.
Arguments squash {_} _.
Inductive sEmpty : SProp :=.
Inductive sUnit : SProp := stt.
Set Primitive Projections.
Record Ssig {A:Type} (P:A->SProp) := Sexists { Spr1 : A; Spr2 : P Spr1 }.
Arguments Sexists {_} _ _ _.
Arguments Spr1 {_ _} _.
Arguments Spr2 {_ _} _.
Lemma Spr1_inj {A P} {a b : @Ssig A P} (e : Spr1 a = Spr1 b) : a = b.
Proof.
destruct a,b;simpl in e.
destruct e. reflexivity.
Defined.
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