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;
reserve N1,N2 for Subgroup of G;

theorem Th51:
  for x being Element of G st x in N ~ H holds x * N meets carr(H)
proof
  let x be Element of G;
  assume x in N ~ H;
  then ex x1 being Element of G st x = x1 & x1 * N meets carr(H);
  hence thesis;
end;
