theorem Th19: :: TOPREAL4:19

for p being Point of (TOP-REAL 2)
for f, h being FinSequence of (TOP-REAL 2)
for r being Real
for u being Point of (Euclid 2) st ( ( p `1 = (f /. (len f)) `1 & p `2 <> (f /. (len f)) `2 ) or ( p `1 <> (f /. (len f)) `1 & p `2 = (f /. (len f)) `2 ) ) & f /. (len f) in Ball (u,r) & p in Ball (u,r) & f is being_S-Seq & (LSeg ((f /. (len f)),p)) /\ (L~ f) = {(f /. (len f))} & h = f ^ <*p*> holds
( h is being_S-Seq & L~ h is_S-P_arc_joining f /. 1,p & L~ h c= (L~ f) \/ (Ball (u,r)) )