Require Export GeoCoq.Elements.OriginalProofs.lemma_samesidecollinear.
Require Export GeoCoq.Elements.OriginalProofs.lemma_PGflip.
Require Export GeoCoq.Elements.OriginalProofs.proposition_41.
Require Export GeoCoq.Elements.OriginalProofs.proposition_38.
Section Euclid.
Context `{Ax:area}.

Lemma proposition_42 :
forall A B C D E J K,
Triangle A B C -> nCol J D K -> Midpoint B E C ->
exists X Z, PG X E C Z /\ EF A B E C X E C Z /\ CongA C E X J D K /\ Col X Z A.