let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over 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 ModuleStr over 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 Def3;

hence ZeroLC V is Linear_Combination of A by Def4; :: thesis: verum

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 ModuleStr over 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 Def3;

hence ZeroLC V is Linear_Combination of A by Def4; :: thesis: verum