Hint Resolve equilateral_swap equilateral_swap_2
equilateral_swap_rot equilateral_rot equilateral_rot_2 : equilateral.

(* Specifications: *)
Lemma equilateral_isosceles_1 :
equilateral A B C ->
isosceles A B C.
Lemma equilateral_isosceles_2 :
equilateral A B C ->
isosceles B C A.
Lemma equilateral_isosceles_3 :
equilateral A B C ->
isosceles C A B.