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 )
assume A1:
angle p1,p2,p3 = (2 * (angle p4,p5,p6)) - (4 * PI )
; :: thesis: contradiction
( angle p4,p5,p6 < 2 * PI & angle p1,p2,p3 >= 0 )
by COMPLEX2:84;
then
(angle p4,p5,p6) * 2 < (2 * PI ) * 2
by XREAL_1:70;
then
((angle p4,p5,p6) * 2) - (4 * PI ) < (4 * PI ) - (4 * PI )
by XREAL_1:11;
hence
contradiction
by A1, COMPLEX2:84; :: thesis: verum