reserve Q,Q1,Q2 for multLoop;
reserve x,y,z,w,u,v for Element of Q;

theorem Th35:
  for H being Subset of Q holds
  for f being Element of Funcs(Q,Q) st
  f in Mlt H holds f is Permutation of Q
proof
  let H be Subset of Q;
  deffunc Phi(Subset of Funcs(Q,Q)) = MltClos1(H,$1);
  consider phi be Function of bool Funcs(Q,Q),bool Funcs(Q,Q)
  such that
  A1: for X being Subset of Funcs(Q,Q) holds phi.X = Phi(X)
  from FUNCT_2:sch 4;
  for S be Subset of Funcs(Q,Q) st phi.S c= S holds Mlt H c= S
  by Th34,A1;
  hence thesis by Th28,A1;
end;
