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(**************************************************************************)
(* *)
(* SMTCoq *)
(* Copyright (C) 2011 - 2019 *)
(* *)
(* See file "AUTHORS" for the list of authors *)
(* *)
(* This file is distributed under the terms of the CeCILL-C licence *)
(* *)
(**************************************************************************)
Require Import
Bool ZArith BVList Logic BVList FArray
SMT_classes SMT_classes_instances ReflectFacts.
Import BVList.BITVECTOR_LIST.
Local Coercion is_true : bool >-> Sortclass.
Infix "-->" := implb (at level 60, right associativity) : bool_scope.
Infix "<-->" := Bool.eqb (at level 60, right associativity) : bool_scope.
Ltac bool2prop :=
repeat
match goal with
| [ |- forall _ : bitvector _, _] => intro
| [ |- forall _ : farray _ _, _] => intro
| [ |- forall _ : _ -> _, _] => intro
| [ |- forall _ : Z, _] => intro
| [ |- forall _ : bool, _] => intro
| [ |- forall _ : Type, _] => intro
| [ p: Type |- context[ forall _ : ?t, _ ] ] => intro
| [ |- forall t : Type, CompDec t -> _ ] => intro
| [ |- CompDec _ -> _ ] => intro
| [ |- context[ bv_ult _ _ ] ] => unfold is_true; rewrite bv_ult_B2P
| [ |- context[ bv_slt _ _ ] ] => unfold is_true; rewrite bv_slt_B2P
| [ |- context[ bv_eq _ _ ] ] => unfold is_true; rewrite bv_eq_reflect
| [ |- context[ equal _ _ ] ] => unfold is_true; rewrite equal_iff_eq
| [ |- context[ Z.ltb _ _ ] ] => unfold is_true; rewrite Z.ltb_lt
| [ |- context[ Z.gtb _ _ ] ] => unfold is_true; rewrite Z.gtb_lt
| [ |- context[ Z.leb _ _ ] ] => unfold is_true; rewrite Z.leb_le
| [ |- context[ Z.geb _ _ ] ] => unfold is_true; rewrite Z.geb_le
| [ |- context[ Z.eqb _ _ ] ] => unfold is_true; rewrite Z.eqb_eq
| [ |- context[?G0 --> ?G1 ] ] =>
unfold is_true; rewrite <- (@reflect_iff (G0 = true -> G1 = true) (G0 --> G1));
[ | apply implyP]
| [ |- context[?G0 || ?G1 ] ] =>
unfold is_true; rewrite <- (@reflect_iff (G0 = true \/ G1 = true) (G0 || G1));
[ | apply orP]
| [ |- context[?G0 && ?G1 ] ] =>
unfold is_true; rewrite <- (@reflect_iff (G0 = true /\ G1 = true) (G0 && G1));
[ | apply andP]
| [ |- context[?G0 <--> ?G1 ] ] =>
unfold is_true; rewrite <- (@reflect_iff (G0 = true <-> G1 = true) (G0 <--> G1));
[ | apply iffP]
| [ |- context[ negb ?G ] ] =>
unfold is_true; rewrite <- (@reflect_iff (G <> true) (negb G));
[ | apply negP]
| [R : CompDec ?t |- context[ CompDec ?t ] ] => exact R
| [R : EqbType ?t |- context[ EqbType ?t ] ] => exact R
| [ |- context[ false = true ] ] => rewrite FalseB
| [ |- context[ true = true ] ] => rewrite TrueB
end.
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