
theorem Th12:
  for L be non empty ZeroStr for p be Polynomial of L st len p = 0
  holds Leading-Monomial(p) = 0_.(L)
proof
  let L be non empty ZeroStr;
  let p be Polynomial of L;
  assume len p = 0;
  then
A1: (0_.(L)).(len p-'1) = p.(len p-'1) by Th5;
  for n be Element of NAT st n <> len p-'1 holds (0_.(L)).n = 0.L by FUNCOP_1:7
;
  hence thesis by A1,Def1;
end;
