
theorem Th11:
  for L be non empty ZeroStr for p be Polynomial of L holds
  Leading-Monomial(p) = 0_.(L)+*(len p-'1,p.(len p-'1))
proof
  let L be non empty ZeroStr;
  let p be Polynomial of L;
  reconsider P=0_.(L)+*(len p-'1,p.(len p-'1)) as sequence of L;
A1: now
    let n be Element of NAT;
    assume n <> len p-'1;
    hence P.n = (0_.(L)).n by FUNCT_7:32
      .= 0.L by FUNCOP_1:7;
  end;
  len p-'1 in NAT;
  then len p-'1 in dom 0_.(L) by NORMSP_1:12;
  then P.(len p-'1) = p.(len p-'1) by FUNCT_7:31;
  hence thesis by A1,Def1;
end;
