Require Export GeoCoq.Elements.OriginalProofs.euclidean_defs.
Require Export GeoCoq.Elements.OriginalProofs.general_tactics.
Ltac remove_double_neg :=
repeat
match goal with
H: ~ ~ ?X |- _ => apply NNPP in H
end.
Section basic_lemmas.
Context `{Ax:euclidean_neutral}.

(* 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.