let A, B, C be Point of (TOP-REAL 2); :: thesis: ( A,B,C is_a_triangle implies the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (A,C,B)) )
assume A,B,C is_a_triangle ; :: thesis: the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (A,C,B))
then A2: ( A,C,B is_a_triangle & B,C,A is_a_triangle ) by MENELAUS:15;
the_diameter_of_the_circumcircle (A,B,C) = the_diameter_of_the_circumcircle (B,C,A) by Thm27
.= - (the_diameter_of_the_circumcircle (C,B,A)) by A2, Thm31 ;
hence the_diameter_of_the_circumcircle (A,B,C) = - (the_diameter_of_the_circumcircle (A,C,B)) by Thm27; :: thesis: verum