reserve m, n for Nat;

theorem Th28:
  for p being Prime, m, d being Nat st p divides m & d
  divides m & not p divides d holds d divides (m div p)
proof
  let p be Prime, m,d be Nat;
  assume that
A1: p divides m and
A2: d divides m and
A3: not p divides d;
  consider z being Nat such that
A4: m = d * z by A2,NAT_D:def 3;
  p divides z by A1,A3,A4,NEWTON:80;
  then consider u being Nat such that
A5: z = p * u by NAT_D:def 3;
  m = d * u * p by A4,A5;
  then m div p = d * u by NAT_D:18;
  hence thesis by NAT_D:def 3;
end;
