reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;

theorem Th3:
  for G being addGroup,A,B,C,D being Subset of G st
  A c= B & C c= D holds A + C c= B + D
  proof
    let G be addGroup,A,B,C,D be Subset of G;
    assume that
A1: A c= B and
A2: C c= D;
    let x be object;
    assume x in A + C;
    then ex a,c be Element of G st x = a + c & a in A & c in C;
    hence thesis by A1,A2;
  end;
