theorem Th21: :: HAHNBAN:21

for V being RealLinearSpace
for X being Subspace of V
for fi being linear-Functional of X
for v being VECTOR of V
for y being VECTOR of (X + (Lin {v})) st v = y & not v in X holds
for r being Real ex psi being linear-Functional of (X + (Lin {v})) st
( psi | the carrier of X = fi & psi . y = r )