theorem Th19: :: PDIFF_8:19

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