theorem Th22: :: TOPREAL4:22

for p being Point of (TOP-REAL 2)
for f being FinSequence of (TOP-REAL 2)
for r being Real
for u being Point of (Euclid 2) st not f /. 1 in Ball (u,r) & f /. (len f) in Ball (u,r) & p in Ball (u,r) & f is being_S-Seq & not p in L~ f holds
ex h being FinSequence of (TOP-REAL 2) st
( L~ h is_S-P_arc_joining f /. 1,p & L~ h c= (L~ f) \/ (Ball (u,r)) )