reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;
reserve L for Subset of Subgroups G;

theorem Th113:
  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 multMagma of H1 = H2 |^ a;
    carr H1 = carr H2 |^ a by A1,Def6;
    hence thesis;
  end;
  given a such that
A2: carr H1 = carr H2 |^ a;
  H1 = H2 |^ a by A2,Def6;
  hence thesis;
end;
