let p1, p2, p3, p4, p5, p6 be Point of (TOP-REAL 2); :: thesis: not angle (p1,p2,p3) = (2 * (angle (p4,p5,p6))) + (4 * PI)
angle (p4,p5,p6) >= 0 by COMPLEX2:70;
then ( 4 * PI >= 2 * PI & ((angle (p4,p5,p6)) * 2) + (4 * PI) >= 0 + (4 * PI) ) by XREAL_1:7, XREAL_1:64;
then A1: ((angle (p4,p5,p6)) * 2) + (4 * PI) >= 2 * PI by XXREAL_0:2;
assume angle (p1,p2,p3) = (2 * (angle (p4,p5,p6))) + (4 * PI) ; :: thesis: contradiction
hence contradiction by A1, COMPLEX2:70; :: thesis: verum