theorem
  j in Seg i & a1 = R1.j & a2 = R2.j implies mlt(R1,R2).j = a1 * a2
proof
  assume j in Seg i;
  then j in Seg len mlt(R1,R2) by CARD_1:def 7;
  then j in dom mlt(R1,R2) by FINSEQ_1:def 3;
  hence thesis by FUNCOP_1:22;
end;
