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 l8_18_existence : forall A B C, ~ Col A B C -> exists X, Col A B X /\ Perp A B C X.