theorem Th16:
  for E be non empty addLoopStr, A, B, C be Subset of E
  holds B c= C implies A + B c= A + C
  proof
    let E be non empty addLoopStr,
    A, B, C be Subset of E;
    assume
    A1: B c= C;
    let x be object;
    assume x in A + B;
    then consider a, b be Element of E such that
    A2: x = a + b & a in A & b in B;
    thus x in A + C by A1,A2;
  end;
