reserve n for Nat;

theorem Th45:
  for f be FinSequence of TOP-REAL 2 for p be Point of TOP-REAL 2
  st p in L~f holds R_Cut(f,p)/.(len R_Cut(f,p)) = p
proof
  let f be FinSequence of TOP-REAL 2;
  let p be Point of TOP-REAL 2;
  assume
A1: p in L~f;
  R_Cut(f,p) is non empty by Th44;
  then len R_Cut(f,p) in dom R_Cut(f,p) by FINSEQ_5:6;
  hence R_Cut(f,p)/.len R_Cut(f,p) = R_Cut(f,p).len R_Cut(f,p) by
PARTFUN1:def 6
    .= p by A1,JORDAN3:24;
end;
