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
  A,B,C is_a_triangle implies -PI < (angle(B,A,C) - angle(C,B,A))/2 < PI
  proof
    assume A,B,C is_a_triangle;
    then (-2) * PI < angle(B,A,C) - angle(C,B,A) < 2 * PI by Th27;
    then (-2) * PI / 2 < (angle(B,A,C) - angle(C,B,A))/2 < (2 * PI) / 2
          by XREAL_1:74;
    hence thesis;
  end;
