let n be Element of NAT ; :: thesis: for S, T being RealNormSpace
for seq being sequence of S
for h being PartFunc of S,T st rng seq c= dom h holds
seq . n in dom h
let S, T be RealNormSpace; :: thesis: for seq being sequence of S
for h being PartFunc of S,T st rng seq c= dom h holds
seq . n in dom h
let seq be sequence of S; :: thesis: for h being PartFunc of S,T st rng seq c= dom h holds
seq . n in dom h
let h be PartFunc of S,T; :: thesis: ( rng seq c= dom h implies seq . n in dom h )
n in NAT ;
then A1: n in dom seq by FUNCT_2:def 1;
assume rng seq c= dom h ; :: thesis: seq . n in dom h
then n in dom (h * seq) by A1, RELAT_1:46;
hence seq . n in dom h by FUNCT_1:21; :: thesis: verum