Section SIGN.
Variable get_sign : C -> option C.
Record sign_theory : Prop := mksign_th {
sign_spec : forall c c', get_sign c = Some c' -> c ?=! -! c' = true
}.
End SIGN.
Definition get_sign_None (c:C) := @None C.

Lemma get_sign_None_th : sign_theory get_sign_None.