reserve x,y,z,x1,x2,y1,y2,z1,z2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  K for Ring;

theorem
  for p,q being FinSequence of K st len p=len q holds
  len mlt(p,q) = len p & len mlt(p,q) = len q
proof
  let p,q be FinSequence of K;
  reconsider r=mlt(p,q) as FinSequence of K;
A1: r=(the multF of K).:(p,q) by FVSUM_1:def 7;
  assume len p=len q;
  hence thesis by A1,FINSEQ_2:72;
end;
