Ltac remove_double_neg :=
repeat
 match goal with
 H: ~ ~ ?X |- _ => apply NNPP in H
end.

(* Specifications: *)
Lemma Col_or_nCol : forall A B C, Col A B C \/ nCol A B C.
Lemma nCol_or_Col : forall A B C, nCol A B C \/ Col A B C.
Lemma eq_or_neq : forall A B, eq A B \/ neq A B.
Lemma neq_or_eq : forall A B, neq A B \/ eq A B.
Lemma Col_nCol_False : forall A B C, nCol A B C -> Col A B C -> False.
Lemma nCol_notCol : forall A B C, ~ Col A B C -> nCol A B C.
Lemma not_nCol_Col : forall A B C, ~ nCol A B C -> Col A B C.
Lemma nCol_not_Col : forall A B C, nCol A B C -> ~ Col A B C.