reserve G for Group;
reserve A,B for non empty Subset of G;
reserve N,H,H1,H2 for Subgroup of G;
reserve x,a,b for Element of G;

theorem Th28:
  for x being Element of G st x in N ~ (A * B) holds x * N meets A * B
proof
  let x be Element of G;
  assume x in N ~ (A * B);
  then consider x1 being Element of G such that
A1: x = x1 & x1 * N meets A * B;
  thus thesis by A1;
end;
