theorem :: HAHNBAN:24

for V being RealNormSpace
for X being Subspace of V
for fi being linear-Functional of X st ( for x being VECTOR of X
for v being VECTOR of V st x = v holds
fi . x <= ||.v.|| ) holds
ex psi being linear-Functional of V st
( psi | the carrier of X = fi & ( for x being VECTOR of V holds psi . x <= ||.x.|| ) )