reserve a,b,i,j,k,l,m,n for Nat;

theorem DLS:
  for f,g,h be complex-valued FinSequence st dom h = dom f /\ dom g holds
    len h = min (len f,len g)
  proof
    let f,g,h be complex-valued FinSequence such that
    A1: dom h = dom f /\ dom g;
    per cases;
    suppose
      B1: len f >= len g; then
      dom f /\ dom g = dom g by FINSEQ_3:30,XBOOLE_1:28; then
      len h = len g by A1,FINSEQ_3:29;
      hence thesis by B1,XXREAL_0:def 9;
    end;
    suppose
      B1: len f < len g; then
      dom f /\ dom g = dom f by FINSEQ_3:30,XBOOLE_1:28; then
      len h = len f by A1,FINSEQ_3:29;
      hence thesis by B1,XXREAL_0:def 9;
    end;
  end;
