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 Th24:
  A,C,B is_a_triangle & angle(A,C,B) < PI implies
  angle(B,A,C) + angle(C,B,A) = PI - angle(A,C,B)
  proof
    assume A,C,B is_a_triangle & angle(A,C,B) < PI;
    then angle(A,C,B) = PI - (angle(C,B,A) + angle(B,A,C)) by Th23;
    hence thesis;
  end;
