let V be RealLinearSpace; :: thesis: for L1, L2 being Linear_Combination of V holds (vector (LC_RLSpace V),L1) - (vector (LC_RLSpace V),L2) = L1 - L2
let L1, L2 be Linear_Combination of V; :: thesis: (vector (LC_RLSpace V),L1) - (vector (LC_RLSpace V),L2) = L1 - L2
- L2 in LinComb V by Def16;
then A1: - L2 in LC_RLSpace V by STRUCT_0:def 5;
- (vector (LC_RLSpace V),L2) = - L2 by Th98
.= vector (LC_RLSpace V),(- L2) by A1, Def1 ;
hence (vector (LC_RLSpace V),L1) - (vector (LC_RLSpace V),L2) = L1 - L2 by Th96; :: thesis: verum