reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;
reserve E for set,
  A for Action of O,E,
  C for Subset of G,
  N1 for normal StableSubgroup of H1;

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;
