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 Th33:
  K is having_valuation implies +infty in rng v
  proof
    assume K is having_valuation;
    then
A1: v.0.K = +infty by Def8;
    dom v = the carrier of K by FUNCT_2:def 1;
    hence thesis by A1,FUNCT_1:def 3;
  end;
