reserve D for non empty set,
  i,j,k for Nat,
  n,m for Nat,
  r for Real,
  e for real-valued FinSequence;

theorem Th47:
  for x,y being FinSequence of REAL,M being Matrix of REAL st len
  x = len M & len y = width M & len y>0 holds |((x*M),y)| = |(x,(M*y))|
proof
  let x,y be FinSequence of REAL, M be Matrix of REAL such that
A1: len x = len M & len y = width M and
A2: len y>0;
  thus |((x*M),y)| = SumAll QuadraticForm(x,M,y) by A1,Th46
    .= |(x,(M*y))| by A1,A2,Th44;
end;
