reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;
reserve x, y, v, u for ExtInt;
reserve
  D for non empty doubleLoopStr,
  A for Subset of D;
reserve K for Field-like non degenerated
  associative add-associative right_zeroed right_complementable
  distributive Abelian non empty doubleLoopStr,
  a, b, c for Element of K;
reserve v for Valuation of K;

theorem Th18:
  K is having_valuation & a <> 0.K implies v.a <> +infty
  proof
    assume K is having_valuation & a <> 0.K;
    then v.a in INT by Def8;
    hence thesis;
  end;
