reserve i,n,m for Nat;

theorem
for m,n be non zero Nat,
    f be PartFunc of REAL m,REAL n, x be Element of REAL m st
  f is_differentiable_in x holds
    diff(f,x) is LinearOperator of m, n
proof
   let m,n be non zero Nat;
   let f be PartFunc of REAL m,REAL n, x be Element of REAL m;
   assume f is_differentiable_in x; then
   diff(f,x) is LinearOperator of REAL-NS m,REAL-NS n by Th18;
   hence thesis by Th14;
end;
