theorem
  r <= i implies [/ r \] <= i
proof
  assume r <= i;
  then
A1: r+1 <= i+1 by XREAL_1:6;
  [/ r \] < r+1 by Def7;
  then [/ r \] < i+1 by A1,XXREAL_0:2;
  then [/ r \] <= i+1-1 by Th50;
  hence thesis;
end;
