intros; intro; subst.
unfold wminus in H.
rewrite wminus_inv in H.
tauto.
Qed.
Ltac word_neq := apply word_neq; let H := fresh "H" in intro H; simpl in H; ring_simplify in H; try discriminate.
Ltac word_contra := match goal with
| [ H : _ <> _ |- False ] => apply H; ring
end.
Ltac word_contra1 := match goal with
| [ H : _ <> _ |- False ] => apply H;
match goal with
| _ => ring
| [ H' : _ = _ |- _ ] => ring [H']
end
end.

Lemma le_neq_lt : forall sz (a b : word sz),
b <= a -> a <> b -> b < a.