let f be non empty FinSequence of (TOP-REAL 2); :: thesis: for p, q being Point of (TOP-REAL 2) st f is almost-one-to-one & f is special & f is unfolded & f is s.n.c. & len f <> 2 & p in L~ f & q in L~ f & p <> q & p <> f . 1 & q <> f . 1 holds
B_Cut (f,p,q) is being_S-Seq
let p, q be Point of (TOP-REAL 2); :: thesis: ( f is almost-one-to-one & f is special & f is unfolded & f is s.n.c. & len f <> 2 & p in L~ f & q in L~ f & p <> q & p <> f . 1 & q <> f . 1 implies B_Cut (f,p,q) 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: len f <> 2 and
A3: p in L~ f and
A4: q in L~ f and
A5: p <> q and
A6: p <> f . 1 and
A7: q <> f . 1 ; :: thesis: B_Cut (f,p,q) is being_S-Seq
B_Cut (f,p,q) is_S-Seq_joining p,q by A1, A2, A3, A4, A5, A6, A7, Th43;
hence B_Cut (f,p,q) is being_S-Seq by JORDAN3:def 2; :: thesis: verum