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 Th88:
  A,B are_conjugated iff ex g st B = A |^ g
proof
  thus A,B are_conjugated implies ex g st B = A |^ g
  proof
    given g such that
A1: A = B |^ g;
    A |^ g" = B by A1,Th54;
    hence thesis;
  end;
  given g such that
A2: B = A |^ g;
  A = B |^ g" by A2,Th54;
  hence thesis;
end;
