theorem Th18: :: PDIFF_8:18

for m, n being non zero Element of NAT
for s being Point of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
for K being Real st ( for i being Element of NAT
for si being Point of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) st si = (Proj (i,n)) * s & 1 <= i & i <= n holds
||.si.|| <= K ) holds
||.s.|| <= n * K