
theorem
  for L be non degenerated non empty multLoopStr_0 holds
  Leading-Monomial(1_.(L)) = 1_.(L)
proof
  let L be non degenerated non empty multLoopStr_0;
A1: now
    let n be Element of NAT;
    assume n <> len (1_.(L))-'1;
    then n <> 1-'1 by Th4;
    then n <> 0 by XREAL_1:232;
    hence (1_.(L)).n = 0.L by POLYNOM3:30;
  end;
  (1_.(L)).(len (1_.(L))-'1) = (1_.(L)).(len (1_.(L))-'1);
  hence thesis by A1,Def1;
end;
