theorem
for f be PartFunc of REAL,REAL n,
    x0 be Real st
 1 <= i & i <= n & f is_differentiable_in x0 holds
   (Proj(i,n)*f) is_differentiable_in x0 &
   Proj(i,n).(diff(f,x0)) = diff((Proj(i,n)*f),x0)
proof
  let f be PartFunc of REAL,REAL n,
      x0 be Real;
  assume
A1: 1 <= i & i <= n & f is_differentiable_in x0;
  then
  consider g be PartFunc of REAL,REAL-NS n such that
A2: f=g & g is_differentiable_in x0;
  diff(f,x0) = diff(g,x0) by A2,Th3;
  hence thesis by A2,A1,Th24;
end;
