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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                                                                          *)
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(*                               Opposite.v                                 *)
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(* G. Huet - V5.8  Nov. 1994 *)
(*    ported V5.10 June 1995 *)
(************)
(* Opposite *)
(************)
Inductive opposite : word -> word -> Prop :=
opp : forall (u v : word) (b : bool), opposite (bit b u) (bit (negb b) v).
Hint Resolve opp.

(* Specifications: *)
Lemma not_opp_empty_r : forall u : word, ~ opposite u empty.
Lemma not_opp_empty_l : forall u : word, ~ opposite empty u.
Lemma not_opp_same :
forall (u v : word) (b : bool), ~ opposite (bit b u) (bit b v).
Lemma alt_neg_opp :
forall (u v : word) (b : bool),
odd u -> alt b u -> odd v -> alt (negb b) v -> opposite u v.
Lemma alt_not_opp :
forall (u v : word) (b : bool), alt b u -> alt b v -> ~ opposite u v.