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 L1, L2 being Linear_Combination of V holds Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2)
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 L1, L2 being Linear_Combination of V holds Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2)
let L1, L2 be Linear_Combination of V; :: thesis: Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2)
Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier (- L2)) by Th23;
hence Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2) by Th38; :: thesis: verum