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;
reserve i for Integer,
  a, b, r, s for Real;

theorem
  frac(r+i) = frac r
proof
  thus frac(r+i) = r+i-[\r+i/]
    .= r+i-([\r/]+i) by Th28
    .= r-[\r/]+i-i
    .= frac r;
end;
