let f be non empty FinSequence of (TOP-REAL 2); for p being Point of (TOP-REAL 2) st f is almost-one-to-one & f is special & f is unfolded & f is s.n.c. & p in L~ f & p <> f . (len f) & p <> f . 1 holds
L_Cut (f,p) is being_S-Seq
let p be Point of (TOP-REAL 2); ( f is almost-one-to-one & f is special & f is unfolded & f is s.n.c. & p in L~ f & p <> f . (len f) & p <> f . 1 implies L_Cut (f,p) is being_S-Seq )
assume that
A1:
( f is almost-one-to-one & f is special & f is unfolded & f is s.n.c. )
and
A2:
p in L~ f
and
A3:
p <> f . (len f)
and
A4:
p <> f . 1
; L_Cut (f,p) is being_S-Seq
L_Cut (f,p) is_S-Seq_joining p,f /. (len f)
by A1, A2, A3, A4, Th40;
hence
L_Cut (f,p) is being_S-Seq
by JORDAN3:def 2; verum