theorem Th30:
  n > 0 implies n in dom (Newton_Coeff n)
  proof
    assume n>0; then
    A1: n in Seg n by FINSEQ_1:3;
    dom (Newton_Coeff n) = Seg (len (Newton_Coeff n)) by FINSEQ_1:def 3
    .= Seg (n+1) by NEWTON:def 5;
    hence thesis by A1,FINSEQ_2:8;
  end;
