theorem lmADD: :: DBLSEQ_2:5

for Rseq1, Rseq2 being Function of [:NAT,NAT:],REAL holds
( dom (Rseq1 + Rseq2) = [:NAT,NAT:] & dom (Rseq1 - Rseq2) = [:NAT,NAT:] & ( for n, m being Nat holds (Rseq1 + Rseq2) . (n,m) = (Rseq1 . (n,m)) + (Rseq2 . (n,m)) ) & ( for n, m being Nat holds (Rseq1 - Rseq2) . (n,m) = (Rseq1 . (n,m)) - (Rseq2 . (n,m)) ) )