Hint Resolve perp_sym perp_left_comm perp_right_comm perp_comm per_perp_in per_perp
perp_in_per perp_in_left_comm perp_in_right_comm perp_in_comm perp_in_sym : perp.
Ltac double A B A' :=
assert (mp:= symmetric_point_construction A B);
elim mp; intros A' ; intro; clear mp.
Section T8_4.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma perp_cong : forall A B P R X,
A <> B -> A <> P ->
Perp A B P A -> Perp A B R B ->
Cong A P B R -> Col A B X -> Bet P X R ->
Cong A R P B.