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;

theorem Th29:
  r < [\ r /] + 1
proof
  r - 1 < [\ r /] by Def6;
  then r - 1 + 1 < [\ r /] + 1 by XREAL_1:6;
  hence thesis;
end;
