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 Th22:
  K is having_valuation & b <> 0.K implies v.(a/b) = v.a - v.b
  proof
    assume
A1: K is having_valuation;
    assume
A2: b <> 0.K;
    thus v.(a/b) = v.a + v.(b") by A1,Def8
    .= v.a - v.b by A1,A2,Th21;
  end;
