Section T8_4.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma Perp_in_cases :
forall X A B C D,
Perp_at X A B C D \/ Perp_at X B A C D \/ Perp_at X A B D C \/ Perp_at X B A D C \/
Perp_at X C D A B \/ Perp_at X C D B A \/ Perp_at X D C A B \/ Perp_at X D C B A ->
Perp_at X A B C D.