let V be RealLinearSpace; :: 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 Th37;

hence Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2) by Th42; :: thesis: verum

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 Th37;

hence Carrier (L1 - L2) c= (Carrier L1) \/ (Carrier L2) by Th42; :: thesis: verum