Require Export C7_DroitesSecantesProp.
Section PARALLEL_SUPERIMPOSED.

(* Specifications: *)
Lemma EquiDirectedCollinearEquiDirected : forall A B C D E : Point,
EquiDirected A B C D ->
Collinear C D E ->
C <> D ->
C <> E ->
EquiDirected A B C E.
Lemma EquiDirectedCollinearCollinearEquiDirected : forall A B C D E F : Point,
EquiDirected A B C D ->
Collinear C D E ->
C <> D ->
Collinear C D F ->
E <> F ->
EquiDirected A B E F.
Lemma TwoPointsSecantLines : forall A B : Point, forall F F' : Figure, forall D : Line F, forall D' : Line F',
Clockwise (LineA F D) (LineB F D) A ->
~Clockwise (LineA F D) (LineB F D) B ->
F' A ->
F' B ->
SecantLines F F' D D'.
Lemma EquiDirectedLineACollinear : forall A : Point, forall F F' : Figure, forall D : Line F, forall D' : Line F',
EquiDirected (LineA F D) (LineB F D) (LineA F' D') (LineB F' D') ->
F A ->
F' A ->
LineA F D <> A ->
F' (LineA F D).
Lemma EquiDirectedLineBCollinear : forall A : Point, forall F F' : Figure, forall D : Line F, forall D' : Line F',
EquiDirected (LineA F D) (LineB F D) (LineA F' D') (LineB F' D') ->
F A ->
F' A ->
LineB F D <> A ->
F' (LineB F D).
Lemma CollinearSuperimposed : forall A : Point, forall F F' : Figure, forall D : Line F, forall D' : Line F',
EquiDirected (LineA F D) (LineB F D) (LineA F' D') (LineB F' D') ->
F A ->
F' A ->
Superimposed F F'.