
theorem Th9:
  for r, s being Real st r >= s holds [\r/] >= [\s/]
proof
  let r, s be Real;
  assume
A1: r >= s;
A2: [\ s /] <= s by INT_1:def 6;
  r-1 < [\ r /] by INT_1:def 6;
  then
A3: r-1+1 < [\ r /]+1 by XREAL_1:6;
  assume [\ r /] < [\ s /];
  then [\ r /] + 1 <= [\ s /] by INT_1:7;
  then r < [\ s /] by A3,XXREAL_0:2;
  hence contradiction by A1,A2,XXREAL_0:2;
end;
