reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem Th33:
  len f <= 2 implies f is s.n.c.
proof
  assume
A1: len f <= 2;
  let i,j be Nat such that
A2: i+1 < j;
  now
    assume that
A3: 1 <= i and
A4: i+1 <= len f and
A5: 1 <= j and
A6: j+1 <= len f;
    j+1 <= 1+1 by A1,A6,XXREAL_0:2;
    then j <= 1 by XREAL_1:6;
    then
A7: j = 1 by A5,XXREAL_0:1;
    i+1 <= 1+1 by A1,A4,XXREAL_0:2;
    then i <= 1 by XREAL_1:6;
    then i = 1 by A3,XXREAL_0:1;
    hence contradiction by A2,A7;
  end;
  then LSeg(f,i) = {} or LSeg(f,j) = {} by TOPREAL1:def 3;
  hence LSeg(f,i) /\ LSeg(f,j) = {};
end;
