Require Export C8_DroitesConfondues.
Section EMBEDDED_TRIANGLES.

(* Specifications: *)
Lemma BetweenClockwiseAMC : forall A B C M : Point,
Clockwise A B C ->
Between A M B ->
Clockwise A M C.
Lemma BetweenClockwiseMBC : forall A B C M : Point,
Clockwise A B C ->
Between A M B ->
Clockwise M B C.
Lemma ClockwiseBetweenAMC : forall A B C M : Point,
Between A M B ->
Clockwise A M C ->
Clockwise A B C.
Lemma ClockwiseBetweenMBC : forall A B C M : Point,
Between A M B ->
Clockwise M B C ->
Clockwise A B C.
Lemma TriangleAMN : forall A B C M N : Point,
Clockwise A B C ->
Between A M B ->
Between A N C ->
Clockwise A M N.
Lemma TriangleBNM : forall A B C M N : Point,
Clockwise A B C ->
Between A M B ->
Between A N C ->
Clockwise B N M.
Lemma TriangleCNM : forall A B C M N : Point,
Clockwise A B C ->
Between A M B ->
Between A N C ->
Clockwise C N M.
Lemma BetweenTriangle : forall A B C D M : Point,
Clockwise A C D ->
Clockwise B C D ->
Between A M B ->
Clockwise M C D.
Lemma TriangleMNP : forall A B C M N P : Point,
Clockwise A B C ->
Between A M B ->
Between B N C ->
Between C P A ->
Clockwise M N P.
Lemma ClockwiseBetween : forall A B C D : Point,
Clockwise A B D ->
Clockwise B C D ->
Collinear A B C ->
Between A B C.