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_cases :
forall A B C D,
Perp A B C D \/ Perp B A C D \/ Perp A B D C \/ Perp B A D C \/
Perp C D A B \/ Perp C D B A \/ Perp D C A B \/ Perp D C B A ->
Perp A B C D.