reserve i,j,k,n for Nat,
  X,Y,a,b,c,x for set,
  r,s for Real;
reserve f,g for FinSequence of TOP-REAL 2;

theorem Th12:
  for f,g st f,g are_in_general_position for k holds L~f /\ LSeg(g
  ,k) is finite
proof
  let f,g;
  assume f,g are_in_general_position;
  then
A1: L~f /\ L~g is finite by Th11;
  let k;
  L~f /\ L~g /\ LSeg(g,k) = L~f /\ (L~g /\ LSeg(g,k)) by XBOOLE_1:16
    .= L~f /\ LSeg(g,k) by TOPREAL3:19,XBOOLE_1:28;
  hence thesis by A1;
end;
