Require Export GeoCoq.Tarski_dev.Ch09_plane.
Require Export GeoCoq.Tarski_dev.Tactics.CoincR_for_cop.
Ltac CopR :=
let tpoint := constr:(Tpoint) in
let col := constr:(Col) in
let cop := constr:(Coplanar) in
assert_ncols; Cop_refl tpoint col cop.
Section T10.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma ex_per_cong : forall A B C D X Y,
A <> B -> X <> Y -> Col A B C -> ~Col A B D ->
exists P, Per P C A /\ Cong P C X Y /\ OS A B P D.