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.

(* Specifications: *)
Lemma equilateral_strict_equilateral :
equilateral_strict A B C ->
equilateral A B C.
Lemma equilateral_cong:
equilateral A B C ->
Cong A B B C /\ Cong B C C A /\ Cong C A A B.
Lemma equilateral_rot :
equilateral A B C ->
equilateral B C A.
Lemma equilateral_swap :
equilateral A B C ->
equilateral B A C.
Lemma equilateral_rot_2 :
equilateral A B C ->
equilateral C B A.
Lemma equilateral_swap_2 :
equilateral A B C ->
equilateral A C B.
Lemma equilateral_swap_rot :
equilateral A B C ->
equilateral C A B.