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
  for f being FinSequence of TOP-REAL 2, p,q being Point of TOP-REAL 2
  st f is being_S-Seq & p in L~f & q in L~f & p<>q holds B_Cut(f,p,q) is
  being_S-Seq
proof
  let f be FinSequence of TOP-REAL 2, p,q be Point of TOP-REAL 2;
  assume that
A1: f is being_S-Seq and
A2: p in L~f and
A3: q in L~f and
A4: p<>q;
  B_Cut(f,p,q) is_S-Seq_joining p,q by A1,A2,A3,A4,Th36;
  hence thesis;
end;
