
theorem ThSc6:
  for L being Z_Lattice, v being Vector of L holds
  <; v, 0.L ;> = 0 & <; 0.L, v ;> = 0
  proof
    let L be Z_Lattice, v be Vector of L;
    thus <; v, 0.L ;> = <; v, v - v ;> by RLVECT_1:15
    .= <; v, v ;> - <; v, v ;> by ThSc5
    .= 0;
    thus <; 0.L, v ;> = <; v - v, v ;> by RLVECT_1:15
    .= <; v, v ;> - <; v, v ;> by ThSc5
    .= 0;
  end;
