let seq1, seq2 be sequence of X; :: thesis: seq1 + seq2 = seq2 + seq1

now :: thesis: for n being Element of NAT holds (seq1 + seq2) . n = (seq2 + seq1) . n

let n be Element of NAT ; :: thesis: (seq1 + seq2) . n = (seq2 + seq1) . n
thus (seq1 + seq2) . n = (seq2 . n) + (seq1 . n) by NORMSP_1:def 2
.= (seq2 + seq1) . n by NORMSP_1:def 2 ; :: thesis: verum

end;

hence seq1 + seq2 = seq2 + seq1 by FUNCT_2:63; :: thesis: verum