(* Could be removed. See gravityCenter.v. *)
Hint Resolve
is_gravity_center_perm_1
is_gravity_center_perm_2
is_gravity_center_perm_3
is_gravity_center_perm_4
is_gravity_center_perm_5 : gravitycenter.
Hint Resolve
is_orthocenter_perm_1
is_orthocenter_perm_2
is_orthocenter_perm_3
is_orthocenter_perm_4
is_orthocenter_perm_5 : Orthocenter.
Hint Resolve
is_circumcenter_perm_1
is_circumcenter_perm_2
is_circumcenter_perm_3
is_circumcenter_perm_4
is_circumcenter_perm_5 : Circumcenter.

Lemma Euler_line :
forall A B C G H O,
~ Col A B C ->
is_gravity_center G A B C ->
is_orthocenter H A B C ->
is_circumcenter O A B C ->
Col G H O.