begin
Lm1:
for V being RealLinearSpace
for V1 being Subset of V
for W being Subspace of V st the carrier of W = V1 holds
V1 is linearly-closed
Lm2:
for V being RealLinearSpace
for W being Subspace of V holds (0. V) + W = the carrier of W
Lm3:
for V being RealLinearSpace
for v being VECTOR of V
for W being Subspace of V holds
( v in W iff v + W = the carrier of W )
:: Introduction of predicate linearly closed subsets of the carrier.
::