let K be non empty non degenerated right_complementable distributive Abelian add-associative right_zeroed associative Field-like doubleLoopStr ; :: thesis: for a being Element of K
for v being Valuation of K st K is having_valuation & a <> 0. K holds
v . a <> +infty
let a be Element of K; :: thesis: for v being Valuation of K st K is having_valuation & a <> 0. K holds
v . a <> +infty
let v be Valuation of K; :: thesis: ( K is having_valuation & a <> 0. K implies v . a <> +infty )
assume ( K is having_valuation & a <> 0. K ) ; :: thesis: v . a <> +infty
then v . a in INT by Def8;
hence v . a <> +infty ; :: thesis: verum