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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** Various syntactic shorthands that are useful with [Program]. *)
Require Export Coq.Program.Tactics.
Set Implicit Arguments.
(** A simpler notation for subsets defined on a cartesian product. *)
Notation "{ ( x , y ) : A | P }" :=
(sig (fun anonymous : A => let (x,y) := anonymous in P))
(x ident, y ident, at level 10) : type_scope.
(** Generates an obligation to prove False. *)
Notation " ! " := (False_rect _ _) : program_scope.
Delimit Scope program_scope with prg.
(** Abbreviation for first projection and hiding of proofs of subset objects. *)
Notation " ` t " := (proj1_sig t) (at level 10, t at next level) : program_scope.
(** Coerces objects to their support before comparing them. *)
Notation " x '`=' y " := ((x :>) = (y :>)) (at level 70) : program_scope.
Require Import Coq.Bool.Sumbool.
(** Construct a dependent disjunction from a boolean. *)
Notation dec := sumbool_of_bool.
(** The notations [in_right] and [in_left] construct objects of a dependent disjunction. *)
(** Hide proofs and generates obligations when put in a term. *)
Notation in_left := (@left _ _ _).
Notation in_right := (@right _ _ _).
(** Extraction directives *)
(*
Extraction Inline proj1_sig.
Extract Inductive unit => "unit" [ "()" ].
Extract Inductive bool => "bool" [ "true" "false" ].
Extract Inductive sumbool => "bool" [ "true" "false" ].
(* Extract Inductive prod "'a" "'b" => " 'a * 'b " [ "(,)" ]. *)
(* Extract Inductive sigT => "prod" [ "" ]. *)
*)
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