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 Th60:
  a in A & b in B implies [.a,b.] in [.A,B.]
proof
  assume a in A & b in B;
  then [.a,b.] in commutators(A,B);
  hence thesis by GROUP_4:29;
end;
