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
dom seq = NAT by FUNCT_2:def 1;
then seq . n in rng seq by FUNCT_1:def 3;
hence for h being PartFunc of S,T st rng seq c= dom h holds
seq . n in dom h ; :: thesis: verum