theorem
  for G being strict Group holds ex H being strict GroupWithOperators of
  O st G = the multMagma of H
proof
  let G be strict Group;
  consider H be non empty HGrWOpStr over O such that
A1: H is strict distributive Group-like associative and
A2: G = the multMagma of H by Lm2;
  reconsider H as strict GroupWithOperators of O by A1;
  take H;
  thus thesis by A2;
end;
