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 Th6:
  tan (2*PI - r) = - tan r
  proof
    tan (2*PI - r) = (- sin(r)) / cos(2*PI-r) by EUCLID10:3
                  .= - sin(r) / cos(2*PI-r)
                  .= - tan (r) by EUCLID10:4;
    hence thesis;
  end;
