theorem ThB113:
  for H1 being strict Subgroup of G holds H1,H2 are_conjugated
  iff carr H1,carr H2 are_conjugated
proof
  let H1 be strict Subgroup of G;
  thus H1,H2 are_conjugated implies carr H1,carr H2 are_conjugated
  proof
    given a such that
A1: the addMagma of H1 = H2 * a;
    carr H1 = carr H2 * a by A1,Def6A;
    hence thesis;
  end;
  given a such that
A2: carr H1 = carr H2 * a;
  H1 = H2 * a by A2,Def6A;
  hence thesis;
end;
