theorem Th52: :: FVALUAT1:52

for K being non empty non degenerated right_complementable distributive Abelian add-associative right_zeroed associative Field-like doubleLoopStr
for a being Element of K
for v being Valuation of K st K is having_valuation holds
( 0 <= v . a iff a is Element of (ValuatRing v) )