Section ABC.
Variable A B C : Tpoint.
Definition isosceles A B C :=
Cong A B B C.
(** In a triangle isosceles in A the altitude wrt. A, is also the bisector and median. *)
Definition equilateral A B C :=
Cong A B B C /\ Cong B C C A.
Definition equilateral_strict A B C :=
equilateral A B C /\ A <> B.
Hint Resolve equilateral_swap equilateral_swap_2
equilateral_swap_rot equilateral_rot equilateral_rot_2 : equilateral.
Hint Resolve equilateral_isosceles_1 equilateral_isosceles_2 equilateral_isosceles_3 : equilateral.
Hint Resolve equilateral_strict_neq : equilateral.
Hint Resolve equilateral_strict_swap_1 equilateral_strict_swap_2
equilateral_strict_swap_3 equilateral_strict_swap_4 equilateral_strict_swap_5 : equilateral.
End ABC.

Lemma conga3_equilateral :
forall A B C,
~ Col A B C ->
CongA B A C A B C ->
CongA A B C B C A ->
equilateral A B C.