reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;
reserve r1,p,p1,g,g1,g2 for Real,
  Y for Subset of REAL;
reserve r, s for Real;

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;
