let p1, p2, p3, p4, p5, p6 be Point of (TOP-REAL 2); :: thesis: not angle p1,p2,p3 = (2 * (angle p4,p5,p6)) + (2 * PI )
angle p4,p5,p6 >= 0 by COMPLEX2:84;
then A1: ((angle p4,p5,p6) * 2) + (2 * PI ) >= 0 + (2 * PI ) by XREAL_1:9;
assume angle p1,p2,p3 = (2 * (angle p4,p5,p6)) + (2 * PI ) ; :: thesis: contradiction
hence contradiction by A1, COMPLEX2:84; :: thesis: verum