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
  for f being Homeomorphism of T for a being Element of HomeoGroup T st
  f = a holds a" = f/"
proof
  let f be Homeomorphism of T;
  set G = HomeoGroup T;
A1: dom f = [#]T by TOPS_2:def 5;
A2: f/" is Homeomorphism of T by Def4;
  then reconsider g = f/" as Element of G by Def5;
A3: rng f = [#]T by TOPS_2:def 5;
  let a be Element of HomeoGroup T such that
A4: f = a;
A5: g * a = f * (f/") by A4,A2,Def5
    .= id T by A3,TOPS_2:52
    .= 1_G by Th32;
  a * g = f/" * f by A4,A2,Def5
    .= id T by A1,A3,TOPS_2:52
    .= 1_G by Th32;
  hence thesis by A5,GROUP_1:5;
end;
