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

theorem Th24:
  for x,y being FinSequence of COMPLEX,a being Element of COMPLEX
  st len x=len y holds mlt(a*x,y) = a*mlt(x,y)
proof
  let x,y be FinSequence of COMPLEX,a be Element of COMPLEX;
  reconsider x9=x as Element of len x-tuples_on COMPLEX by FINSEQ_2:92;
  reconsider y9=y as Element of len y-tuples_on COMPLEX by FINSEQ_2:92;
  assume len x=len y;
  then mlt(a*x,y) = a*mlt(x9,y9) by Th15
    .= a*mlt(x,y);
  hence thesis;
end;
