
theorem Th9:
  for j,k,l being Nat st 0 < l < j holds not j divides j*k+l
proof
  let j,k,l be Nat;
  set i = j*k+l;
  assume that
A3: 0<l and
A2: l<j;
  assume j divides i;
  then i = j * (i div j) by NAT_D:3;
  then j * (i div j) = j * (i div j) + l by A2,NAT_D:def 1;
  hence contradiction by A3;
end;
