theorem Th72: :: FVALUAT1:72

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 & v . a = 0 holds
( a is Element of (ValuatRing v) & a " is Element of (ValuatRing v) )