reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th57:
  for x being FinSequence of REAL, A,B being Matrix of REAL st 
  len x = len A & width A = len B holds x*(A*B) = (x*A)*B
proof
  let x be FinSequence of REAL,A,B be Matrix of REAL;
  assume that
A1: len x=len A and
A2: width A=len B;
  width LineVec2Mx x=len x by MATRIXR1:def 10;
  hence x*(A*B) = Line((LineVec2Mx x)*A*B,1) by A1,A2,MATRIX_3:33
    .=(x*A)*B by A1,Th56;
end;
