
theorem
for f1,f2 be without+infty Function of [:NAT,NAT:],ExtREAL, n,m be Nat holds
  (f1+f2).(n,m) = f1.(n,m) + f2.(n,m)
proof
   let f1,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;
