End T7_1.
Hint Resolve l7_13 : cong.
Hint Resolve l7_2 l7_3_2 : midpoint.
Ltac Midpoint := auto with midpoint.
Section T7_2.
Context {Tn:Tarski_neutral_dimensionless}.
Context {TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality Tn}.

(* Specifications: *)
Lemma Mid_cases :
forall A B C,
Midpoint A B C \/ Midpoint A C B ->
Midpoint A B C.
Lemma Mid_perm :
forall A B C,
Midpoint A B C ->
Midpoint A B C /\ Midpoint A C B.
Lemma l7_17 : forall P P' A B, Midpoint A P P' -> Midpoint B P P' -> A=B.
Lemma l7_17_bis : forall P P' A B, Midpoint A P P' -> Midpoint B P' P -> A=B.
Lemma l7_20 : forall M A B,
Col A M B -> Cong M A M B -> A=B \/ Midpoint M A B.
Lemma l7_20_bis : forall M A B, A<>B ->
Col A M B -> Cong M A M B -> Midpoint M A B.
Lemma cong_col_mid : forall A B C,
A <> C -> Col A B C -> Cong A B B C ->
Midpoint B A C.
Lemma l7_21 : forall A B C D P,
~ Col A B C -> B<>D ->
Cong A B C D -> Cong B C D A ->
Col A P C -> Col B P D ->
Midpoint P A C /\ Midpoint P B D.
Lemma l7_22_aux : forall A1 A2 B1 B2 C M1 M2,
Bet A1 C A2 -> Bet B1 C B2 ->
Cong C A1 C B1 -> Cong C A2 C B2 ->
Midpoint M1 A1 B1 -> Midpoint M2 A2 B2 ->
Le C A1 C A2 ->
Bet M1 C M2.