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 Th13:
  (inverse_op G)" = inverse_op G
proof
  set f = inverse_op G;
A1: dom f = the carrier of G by FUNCT_2:def 1;
A2: now
    let x be object;
    assume x in dom f;
    then reconsider g = x as Element of G;
A3: f.(g") = g"" by GROUP_1:def 6
      .= g;
    thus f.x = g" by GROUP_1:def 6
      .= f".x by A1,A3,FUNCT_1:32;
  end;
  thus thesis by A1,A2;
end;
