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 Th50:
  A c= B & C c= D implies commutators(A,C) c= commutators(B,D)
proof
  assume
A1: A c= B & C c= D;
  let x be object;
  assume x in commutators(A,C);
  then ex a,c st x = [.a,c.] & a in A & c in C;
  hence thesis by A1;
end;
