let A, B, C be Point of (TOP-REAL 2); ( A,B,C is_a_triangle implies the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (C,B,A)) )
assume
A,B,C is_a_triangle
; the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (C,B,A))
then
the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (A,C,B))
by Thm32;
hence
the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (C,B,A))
by Thm27; verum