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Require Export Coq.subtac.SubtacTactics.
Set Implicit Arguments.
Notation " {{ x }} " := (tt : { y : unit | x }).
Notation "{ ( x , y ) : A | P }" :=
(sig (fun anonymous : A => let (x,y) := anonymous in P))
(x ident, y ident) : type_scope.
Notation " ! " := (False_rect _ _).
Notation " ` t " := (proj1_sig t) (at level 10) : core_scope.
Notation "( x & ? )" := (@exist _ _ x _) : core_scope.
(** Coerces objects before comparing them *)
Notation " x '`=' y " := ((x :>) = (y :>)) (at level 70).
(** Quantifying over subsets *)
Notation "'fun' { x : A | P } => Q" :=
(fun x:{x:A|P} => Q)
(at level 200, x ident, right associativity).
Notation "'forall' { x : A | P } , Q" :=
(forall x:{x:A|P}, Q)
(at level 200, x ident, right associativity).
Require Import Coq.Bool.Sumbool.
Notation "'dec'" := (sumbool_of_bool) (at level 0).
(** Default simplification tactic. *)
Ltac subtac_simpl := simpl ; intros ; destruct_conjs ; simpl in * ; try subst ;
try (solve [ red ; intros ; discriminate ]) ; auto with *.
(** Extraction directives *)
Extraction Inline proj1_sig.
Extract Inductive unit => "unit" [ "()" ].
Extract Inductive bool => "bool" [ "true" "false" ].
Extract Inductive sumbool => "bool" [ "true" "false" ].
Axiom pair : Type -> Type -> Type.
Extract Constant pair "'a" "'b" => " 'a * 'b ".
Extract Inductive prod => "pair" [ "" ].
Extract Inductive sigT => "pair" [ "" ].
Require Export ProofIrrelevance.
Delimit Scope program_scope with program.
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