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 L being Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
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 L being Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
let L be Linear_Combination of V; :: thesis: ( Carrier L = {} implies Sum L = 0. V )
assume Carrier L = {} ; :: thesis: Sum L = 0. V
then L = ZeroLC V by Def3;
hence Sum L = 0. V by Lm1; :: thesis: verum