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 midpoint_preserves_per : forall A B C A1 B1 C1 M,
Per A B C ->
Midpoint M A A1 ->
Midpoint M B B1 ->
Midpoint M C C1 ->
Per A1 B1 C1.