reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th59:
  (Omega).G "\/" H = (Omega).G & H "\/" (Omega).G = (Omega).G
proof
A1: (the carrier of (Omega). G) \/ carr H = [#] the carrier of G by SUBSET_1:11
;
  hence (Omega).G "\/" H = (Omega).G by Th31;
  thus thesis by A1,Th31;
end;
