reserve i,n,m for Nat;

theorem Th14:
for f be set holds f is LinearOperator of m,n
  iff f is LinearOperator of REAL-NS m,REAL-NS n
proof
   let f be set;
   REAL m = the carrier of REAL-NS m
   & REAL n = the carrier of REAL-NS n by REAL_NS1:def 4;
   hence f is additive homogeneous Function of REAL m,REAL n
     iff f is additive homogeneous Function of REAL-NS m,REAL-NS n
       by Th12,Th13;
end;
