theorem Th27: :: VECTSP10:27

for K being Field
for V being VectSp of K
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 Element of K ex psi being linear-Functional of (X + (Lin {v})) st
( psi | the carrier of X = fi & psi . y = r )