reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem Th44:
  for G being UnContinuous TopGroup holds inverse_op G is Homeomorphism of G
proof
  let G be UnContinuous TopGroup;
  set f = inverse_op G;
  thus
 dom f = [#]G & rng f = [#]G & f is one-to-one by FUNCT_2:def 1,def 3;
  thus f is continuous by Def7;
  f = (f qua Function)" by Th13
    .= f/" by TOPS_2:def 4;
  hence thesis by Def7;
end;
