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 holds Carrier (- L) = Carrier L
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 holds Carrier (- L) = Carrier L
let L be Linear_Combination of V; :: thesis: Carrier (- L) = Carrier L
( Carrier (- L) c= Carrier L & Carrier (- (- L)) c= Carrier (- L) ) by Th28;
hence Carrier (- L) = Carrier L ; :: thesis: verum