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 Th59:
  the carrier of H |^ a = a" * H * a
proof
  thus the carrier of H |^ a = carr(H) |^ a by Def6
    .= a" * H * a by Th50;
end;
