
theorem
for f1 be without-infty Function of [:NAT,NAT:],ExtREAL,
    f2 be without+infty Function of [:NAT,NAT:],ExtREAL, n,m be Nat holds
  (f1-f2).(n,m) = f1.(n,m) - f2.(n,m) & (f2-f1).(n,m) = f2.(n,m) - f1.(n,m)
proof
   let f1 be without-infty Function of [:NAT,NAT:],ExtREAL,
       f2 be without+infty Function of [:NAT,NAT:],ExtREAL, n,m be Nat;
A1:n in NAT & m in NAT by ORDINAL1:def 12; then
   reconsider z = [n,m] as Element of [:NAT,NAT:] by ZFMISC_1:87;
   [n,m] in [:NAT,NAT:] by A1,ZFMISC_1:87;
   hence thesis by Th7;
end;
