let V be Z_Module; :: thesis: for L1, L2 being Z_Linear_Combination of V holds Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2)
let L1, L2 be Z_Linear_Combination of V; :: thesis: Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2)
Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier (- L2)) by Th26;
hence Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2) by Th29; :: thesis: verum