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 VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for L being Linear_Combination of V st Carrier L = {} holds
Sum L = 0. V
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of 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 Def6;
hence Sum L = 0. V by Lm1; :: thesis: verum