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

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