reserve r1,r2 for Real;
reserve n,i,i1,i2,j for Nat;
reserve D for non empty set;
reserve f for FinSequence of D;

theorem Th34:
  for f being FinSequence of TOP-REAL 2, p being Point of TOP-REAL
  2 st f is being_S-Seq & p in L~f & p<>f.len f holds L_Cut(f,p) is being_S-Seq
proof
  let f be FinSequence of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume that
A1: f is being_S-Seq and
A2: p in L~f and
A3: p<>f.len f;
  L_Cut(f,p) is_S-Seq_joining p,f/.len f by A1,A2,A3,Th33;
  hence thesis;
end;
