reserve A,B,C,D,E,F,G for Point of TOP-REAL 2;

theorem
  A,B,C are_mutually_distinct & angle (A,B,C) > PI implies
    angle (B,C,A) > PI & angle (C,A,B) > PI
proof
  assume
A1:  A,B,C are_mutually_distinct & angle (A,B,C) > PI;
  set z1 = euc2cpx(A);
  set z2 = euc2cpx(B);
  set z3 = euc2cpx(C);
  z1 <> z2 & z2 <> z3 & z1 <> z3 & angle (z1,z2,z3) > PI
    by A1,EUCLID_3:4,EUCLID_3:def 4;
  then angle (z2,z3,z1) > PI & angle (z3,z1,z2) > PI by COMPLEX2:85;
  hence thesis by EUCLID_3:def 4;
end;
