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 f /. (len f) in Ball (u,r) & p in Ball (u,r) & |[(p `1),((f /. (len f)) `2)]| in Ball (u,r) & f is being_S-Seq & p `1 <> (f /. (len f)) `1 & p `2 <> (f /. (len f)) `2 & h = f ^ <*|[(p `1),((f /. (len f)) `2)]|,p*> & ((LSeg ((f /. (len f)),|[(p `1),((f /. (len f)) `2)]|)) \/ (LSeg (|[(p `1),((f /. (len f)) `2)]|,p))) /\ (L~ f) = {(f /. (len f))} holds
( L~ h is_S-P_arc_joining f /. 1,p & L~ h c= (L~ f) \/ (Ball (u,r)) )