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 Th26:
  K is having_valuation & b <> 0.K & v.(a/b) <= 0 implies v.a <= v.b
  proof
    assume that
A1: K is having_valuation and
A2: b <> 0.K and
A3: v.(a/b) <= 0;
A4: a <> 0.K by A1,Def8,A3;
    then 0 <= v.(b/a) by A1,A2,A3,Th25;
    hence v.a <= v.b by A1,A4,Th24;
  end;
