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
  1 <= i & i+1 <= len f implies LSeg(f/.i,f/.(i+1)) c= L~f
proof
  assume that
A1: 1 <= i and
A2: i+1 <= len f;
  LSeg(f,i) = LSeg(f/.i,f/.(i+1)) by A1,A2,TOPREAL1:def 3;
  hence thesis by TOPREAL3:19;
end;
