theorem Th25: :: NORMSP_2:25

for X being RealNormSpace
for S being Subset-Family of (TopSpaceNorm X)
for St being Subset-Family of (LinearTopSpaceNorm X)
for x being Point of (TopSpaceNorm X)
for xt being Point of (LinearTopSpaceNorm X) st S = St & x = xt holds
( St is Basis of iff S is Basis of )