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.
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.
Lemma equilateral_strict_neq : equilateral_strict A B C -> A <> B /\ B <> C /\ A <> C.
Lemma equilateral_strict_swap_1 : equilateral_strict A B C -> equilateral_strict A C B.
Lemma equilateral_strict_swap_2 : equilateral_strict A B C -> equilateral_strict B A C.
Lemma equilateral_strict_swap_3 : equilateral_strict A B C -> equilateral_strict B C A.
Lemma equilateral_strict_swap_4 : equilateral_strict A B C -> equilateral_strict C A B.
Lemma equilateral_strict_swap_5 : equilateral_strict A B C -> equilateral_strict C B A.
Lemma equilateral_strict__not_col : equilateral_strict A B C -> ~ Col A B C.
Lemma equilateral_strict_conga_1 : equilateral_strict A B C -> CongA C A B A C B.
Lemma equilateral_strict_conga_2 : forall A B C, equilateral_strict A B C -> CongA B A C A B C.
Lemma equilateral_strict_conga_3 : forall A B C, equilateral_strict A B C -> CongA C B A B C A.
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.