theorem Th38:
  K is having_valuation implies
  (v.a = +infty iff normal-valuation(v).a = +infty)
  proof
    assume
A1: K is having_valuation;
    set f = normal-valuation(v);
    set l = least-positive(rng v);
A2: v.a = (f.a)*l by A1,Def10;
    l is integer by A1,Th35;
    hence v.a = +infty implies f.a = +infty by A2,XXREAL_3:69;
    thus thesis by A2,XXREAL_3:def 5;
  end;
