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;
