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author | Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
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committer | Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
commit | 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 (patch) | |
tree | 631ad791a7685edafeb1fb2e8faeedc8379318ae /plugins/setoid_ring/Ring.v | |
parent | da178a880e3ace820b41d38b191d3785b82991f5 (diff) |
Imported Upstream snapshot 8.3~beta0+13298
Diffstat (limited to 'plugins/setoid_ring/Ring.v')
-rw-r--r-- | plugins/setoid_ring/Ring.v | 44 |
1 files changed, 44 insertions, 0 deletions
diff --git a/plugins/setoid_ring/Ring.v b/plugins/setoid_ring/Ring.v new file mode 100644 index 00000000..d01b1625 --- /dev/null +++ b/plugins/setoid_ring/Ring.v @@ -0,0 +1,44 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +Require Import Bool. +Require Export Ring_theory. +Require Export Ring_base. +Require Export InitialRing. +Require Export Ring_tac. + +Lemma BoolTheory : + ring_theory false true xorb andb xorb (fun b:bool => b) (eq(A:=bool)). +split; simpl in |- *. +destruct x; reflexivity. +destruct x; destruct y; reflexivity. +destruct x; destruct y; destruct z; reflexivity. +reflexivity. +destruct x; destruct y; reflexivity. +destruct x; destruct y; reflexivity. +destruct x; destruct y; destruct z; reflexivity. +reflexivity. +destruct x; reflexivity. +Qed. + +Definition bool_eq (b1 b2:bool) := + if b1 then b2 else negb b2. + +Lemma bool_eq_ok : forall b1 b2, bool_eq b1 b2 = true -> b1 = b2. +destruct b1; destruct b2; auto. +Qed. + +Ltac bool_cst t := + let t := eval hnf in t in + match t with + true => constr:true + | false => constr:false + | _ => constr:NotConstant + end. + +Add Ring bool_ring : BoolTheory (decidable bool_eq_ok, constants [bool_cst]). |