theorem Th8: :: RSSPACE3:8

for NRM being RealNormSpace
for seq being sequence of NRM holds
( seq is Cauchy_sequence_by_Norm iff for r being Real st r > 0 holds
ex k being Nat st
for n, m being Nat st n >= k & m >= k holds
||.((seq . n) - (seq . m)).|| < r )