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

theorem Th40:
  for F being FinSequence of COMPLEX,M being Matrix of COMPLEX st
  len F=width M holds mlt(F,(Line((M*'),i))*') = mlt(Line((M*'),i),(F*'))*'
proof
  let F be FinSequence of COMPLEX,M be Matrix of COMPLEX;
  assume
A1: len F=width M;
  len (Line((M*'),i))=width (M*') by MATRIX_0:def 7
    .= width M by Def1;
  hence thesis by A1,Th22;
end;
