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;

theorem Th102:
  for H1,H2 being strict Subgroup of G holds H1,H2 are_conjugated
  iff ex g st H2 = H1 |^ g
proof
  let H1,H2 be strict Subgroup of G;
  thus H1,H2 are_conjugated implies ex g st H2 = H1 |^ g
  proof
    given g such that
A1: the multMagma of H1 = H2 |^ g;
    H1 |^ g" = H2 by A1,Th62;
    hence thesis;
  end;
  given g such that
A2: H2 = H1 |^ g;
  H1 = H2 |^ g" by A2,Th62;
  hence thesis;
end;
