Ltac assert_all := treat_equalities; assert_cols_perm; assert_diffs; assert_congs_perm.

Lemma triangle_mid_par_flat_cong_aux : forall A B C P Q R, B <> A -> Col A B C -> Midpoint P B C -> Midpoint Q A C -> Midpoint R A B -> Par A B Q P /\ Cong A R P Q /\ Cong B R P Q.