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.

Lemma equilateral_isosceles_3 :
equilateral A B C ->
isosceles C A B.