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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 *)
(************************************************************************)
(* Certified Haskell Prelude.
* Author: Matthieu Sozeau
* Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
* 91405 Orsay, France *)
Require Import Coq.Program.Program.
Set Implicit Arguments.
Unset Strict Implicit.
Require Import Coq.Classes.SetoidTactics.
Goal not True == not (not False) -> ((not True -> True)) \/ True.
intros.
clrewrite H.
clrewrite <- H.
right ; auto.
Defined.
Definition reduced_thm := Eval compute in Unnamed_thm.
(* Print reduced_thm. *)
Lemma foo [ Setoid a R ] : True. (* forall x y, R x y -> x -> y. *)
Proof.
intros.
Print respect2.
pose setoid_morphism.
pose (respect2 (b0:=b)).
simpl in b0.
unfold binary_respectful in b0.
pose (arrow_morphism R).
pose (respect2 (b0:=b1)).
unfold binary_respectful in b2.
pose (eq_morphism (A:=a)).
pose (respect2 (b0:=b3)).
unfold binary_respectful in b4.
exact I.
Qed.
Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C.
intros.
Set Printing All.
Print iff_morphism.
clrewrite H.
clrewrite H'.
reflexivity.
Defined.
Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C.
intros.
rewrite H.
rewrite H'.
reflexivity.
Defined.
Require Import Setoid_tac.
Require Import Setoid_Prop.
(* Print Unnamed_thm0. *)
(* Print Unnamed_thm1. *)
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