
theorem
  for i, j being Integer st 0<=i & i<j holds i div j = 0
proof
  let i, j be Integer;
  assume
A1: 0 <= i & i < j;
  then i / j < j / j by XREAL_1:74;
  then i / j < 0+1 by A1,XCMPLX_1:60;
  then i/j - 1 < 0 by XREAL_1:19;
  then [\ i / j /] = 0 by A1,INT_1:def 6;
  hence thesis by INT_1:def 9;
end;
