reserve n for Nat;

theorem Th39:
  for f be FinSequence of TOP-REAL 2 for p be Point of TOP-REAL 2
  st f is almost-one-to-one special unfolded s.n.c. & p in L~f & p<>f.1 holds
  R_Cut(f,p) is_S-Seq_joining f/.1,p
proof
  let f be FinSequence of TOP-REAL 2;
  let p be Point of TOP-REAL 2;
  assume that
A1: f is almost-one-to-one special unfolded s.n.c. and
A2: p in L~f and
A3: p<>f.1;
  R_Cut(f,p)=mid(f,1,Index(p,f))^<*p*> by A3,JORDAN3:def 4;
  hence thesis by A1,A2,A3,Th35;
end;
