Require Export D2_Axe.
Section TRIANGLE_PROPERTIES.

(* Specifications: *)
Lemma TriangleSpecComm : forall A B C : Point,
A <> B ->
B <> C ->
C <> A ->
TriangleSpec (Distance A B) (Distance B C) (Distance C A) ->
TriangleSpec (Distance A B) (Distance C A) (Distance B C) .
Lemma EqualTriangleClockwise : forall A B C D E : Point,
Clockwise A B C ->
Distance A B = Distance D E ->
{F : Point |
Clockwise D E F /\
Distance B C = Distance E F /\
Distance C A = Distance F D}.
Lemma EqualTriangleAntiClockwise : forall A B C D E : Point,
Clockwise A B C ->
Distance A B = Distance D E ->
{F : Point |
Clockwise D F E /\
Distance B C = Distance E F /\
Distance C A = Distance F D}.
Lemma ExistsCongruentStrictTriangle : forall A B C D E : Point,
Clockwise A B C ->
Distance A B = Distance D E ->
{F : Point | CongruentStrictTriangles A B C D E F /\ Clockwise D E F}.