reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem Th23:
  A,C,B is_a_triangle & angle(A,C,B) < PI
  implies
  angle(A,C,B) = PI - (angle(C,B,A) + angle(B,A,C))
  proof
    assume that
A1: A,C,B is_a_triangle and
A2: angle(A,C,B) < PI;
    A,C,B are_mutually_distinct by A1,EUCLID_6:20;
    then angle(A,C,B) + angle (C,B,A) + angle (B,A,C) = PI by A2,EUCLID_3:47;
    hence thesis;
  end;
