theorem Th18: :: TOPREAL4:18

for p being Point of (TOP-REAL 2)
for f being FinSequence of (TOP-REAL 2) st p <> f /. 1 & f is being_S-Seq & p in L~ f holds
ex h being FinSequence of (TOP-REAL 2) st
( h is being_S-Seq & h /. 1 = f /. 1 & h /. (len h) = p & L~ h is_S-P_arc_joining f /. 1,p & L~ h c= L~ f )