let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF
for A being Subset of V holds ZeroLC V is Linear_Combination of A
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for A being Subset of V holds ZeroLC V is Linear_Combination of A
let A be Subset of V; :: thesis: ZeroLC V is Linear_Combination of A
( Carrier (ZeroLC V) = {} & {} c= A ) by Def6, XBOOLE_1:2;
hence ZeroLC V is Linear_Combination of A by Def7; :: thesis: verum