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 Th29:
  A,B,C is_a_triangle & angle(B,A,C) < PI implies
  -PI/2 < (angle(B,A,C) - angle(C,B,A))/2 < PI/2
  proof
    assume A,B,C is_a_triangle & angle(B,A,C) < PI;
    then -PI < angle(B,A,C) - angle(C,B,A) < PI by Th28;
    then (-PI) / 2 < (angle(B,A,C) - angle(C,B,A))/2 < PI / 2 by XREAL_1:74;
    hence thesis;
  end;
