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 Th25:
  [\ r /] = r iff r is integer
proof
  r is Integer implies [\ r /] = r
  proof
    r + 0 < r + 1 by XREAL_1:6;
    then r - 1 < r + 1 - 1 by XREAL_1:9;
    hence thesis by Def6;
  end;
  hence thesis;
end;
