reserve n for Nat;

theorem Th20:
  for f be FinSequence of TOP-REAL 2 st f is weakly-one-to-one for
p,q be Point of TOP-REAL 2 st p in L~f & q in L~f holds B_Cut(f,p,q)/.len B_Cut
  (f,p,q) = q
proof
  let f be FinSequence of TOP-REAL 2;
  assume
A1: f is weakly-one-to-one;
  let p,q be Point of TOP-REAL 2 such that
A2: p in L~f and
A3: q in L~f;
A4: B_Cut(f,q,p) <> {} by Th3;
  B_Cut(f,p,q) = Rev B_Cut(f,q,p) by A1,A2,A3,Th17;
  hence B_Cut(f,p,q)/.len B_Cut(f,p,q) = Rev B_Cut(f,q,p)/.len B_Cut(f,q,p) by
FINSEQ_5:def 3
    .= B_Cut(f,q,p)/.1 by A4,FINSEQ_5:65
    .= q by A1,A2,A3,Th19;
end;
