 reserve R for domRing;
 reserve p for odd prime Nat, m for positive Nat;

theorem Th14:
  for p1, q1 be sequence of INT.Ring holds (p1 *' q1).0 = (p1.0) * q1.0
    proof
      let p1, q1 be sequence of INT.Ring;
      consider r be FinSequence of the carrier of INT.Ring such that
A1:   len r = 0+1 & (p1*'q1).0 = Sum r &
      for k be Element of NAT st k in dom r holds
      r.k = p1.(k-'1) * q1.(0+1-'k) by POLYNOM3:def 9;
A2:   r = <* r.1 *> by A1,FINSEQ_1:40;
      dom r = Seg 1 by A1,FINSEQ_1:def 3; then
      1 in dom r; then
      r.1 = p1.(1-'1) * q1.(0+1-'1) by A1
      .= (p1.0) * q1.(0+0);
      hence thesis by A1,A2,RLVECT_1:44;
    end;
