reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem
  for F1,F2,F3 being FinSequence of COMPLEX st len F1 = len F2 & len F2
  = len F3 holds mlt(F1,mlt(F2,F3)) = mlt(mlt(F1,F2),F3)
proof
  let F1,F2,F3 be FinSequence of COMPLEX;
  assume that
A1: len F1=len F2 and
A2: len F2=len F3;
  reconsider f3=F3 as Element of (len F3)-tuples_on COMPLEX by FINSEQ_2:92;
  reconsider f2=F2 as Element of (len F2)-tuples_on COMPLEX by FINSEQ_2:92;
  reconsider f1=F1 as Element of (len F1)-tuples_on COMPLEX by FINSEQ_2:92;
  thus mlt(F1,mlt(F2,F3)) = multcomplex.:(multcomplex.:(f1,f2),f3) by A1,A2,
FINSEQOP:28
    .= mlt(mlt(F1,F2),F3);
end;
