Require Export B7_Triangle_Equilateral.
Section POINT_PROPERTIES.

(* Specifications: *)
Lemma ExistsHalfLineEquidistant : forall A B C D : Point,
A <> B ->
C <> D ->
{E : Point |
HalfLine A B E /\
Distance A E = Distance C D}.
Lemma HalfLineEquidistantEqual : forall A B C : Point,
A <> B ->
HalfLine A B C ->
Distance A B = Distance A C ->
B = C.
Lemma ExistsBetweenEquidistant : forall A B C D : Point,
A <> B ->
C <> D ->
{E : Point |
Between E A B /\
Distance A E = Distance C D}.
Lemma ExistsEquidistantBetween : forall A B C D : Point,
A <> B ->
C <> D ->
{E : Point |
Between A B E  /\
Distance B E = Distance C D}.
Lemma CentralSymetPoint : forall A B : Point,
A <> B ->
{C : Point | Distance A B = Distance B C /\ Between A B C}.
Lemma CoordinatePoint : forall A B : Point,
A <> B ->
{C : Point | HalfLine Oo Uu C /\ Distance Oo C = Distance A B}.