
theorem
  for L being non empty 1-sorted, N being non empty NetStr over L for i
  being Element of N holds the carrier of N|i = { y where y is Element of N : i
  <= y }
proof
  let L be non empty 1-sorted, N be non empty NetStr over L, i be Element of N;
  thus the carrier of N|i c= { y where y is Element of N : i <= y }
  proof
    let q be object;
    assume q in the carrier of N|i;
    then ex y being Element of N st y = q & i <= y by Def7;
    hence thesis;
  end;
  let q be object;
  assume q in { y where y is Element of N : i <= y };
  then ex y being Element of N st q = y & i <= y;
  hence thesis by Def7;
end;
