take sc ; :: thesis: sc is bounded
take 1 ; :: according to COMSEQ_2:def 3 :: thesis: for n being Element of NAT holds |.(sc . n).| < 1
let n be Element of NAT ; :: thesis: |.(sc . n).| < 1
thus |.(sc . n).| < 1 by COMPLEX1:44, FUNCOP_1:7; :: thesis: verum