reserve i,j for Nat;
reserve A,B for Ring;
reserve K, L for Field;

theorem Lm37:
  for K be Field, p be Element of Polynom-Ring K st p <> 0_.K holds
  p is non zero Element of the carrier of Polynom-Ring K
  proof
    let K;
    let p be Element of Polynom-Ring K;
    assume
A0: p <> 0_.K;
    assume
A1: not(p is non zero Element of the carrier of Polynom-Ring K);
    reconsider p as Element of the carrier of Polynom-Ring K;
    p is zero by A1;
    hence contradiction by A0;
  end;
