theorem
for
A,
B,
C being
Point of
(TOP-REAL 2) st
A,
B,
C are_mutually_distinct &
angle (
A,
B,
C)
= 0 & not (
angle (
B,
C,
A)
= 0 &
angle (
C,
A,
B)
= PI ) holds
(
angle (
B,
C,
A)
= PI &
angle (
C,
A,
B)
= 0 &
((angle (A,B,C)) + (angle (B,C,A))) + (angle (C,A,B)) = PI )