reserve x,y for set,
  k,n for Nat,
  i for Integer,
  G for Group,
  a,b,c ,d,e for Element of G,
  A,B,C,D for Subset of G,
  H,H1,H2,H3,H4 for Subgroup of G ,
  N1,N2 for normal Subgroup of G,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th65:
  a in H1 & b in H2 implies [.a,b.] in [.H1,H2.]
proof
  assume a in H1 & b in H2;
  then a in carr H1 & b in carr H2 by STRUCT_0:def 5;
  hence thesis by Th60;
end;
