let V be Z_Module; :: thesis: for L1, L2 being Z_Linear_Combination of V
for A being Subset of V st L1 is Z_Linear_Combination of A & L2 is Z_Linear_Combination of A holds
L1 - L2 is Z_Linear_Combination of A
let L1, L2 be Z_Linear_Combination of V; :: thesis: for A being Subset of V st L1 is Z_Linear_Combination of A & L2 is Z_Linear_Combination of A holds
L1 - L2 is Z_Linear_Combination of A
let A be Subset of V; :: thesis: ( L1 is Z_Linear_Combination of A & L2 is Z_Linear_Combination of A implies L1 - L2 is Z_Linear_Combination of A )
assume that
A1: L1 is Z_Linear_Combination of A and
A2: L2 is Z_Linear_Combination of A ; :: thesis: L1 - L2 is Z_Linear_Combination of A
- L2 is Z_Linear_Combination of A by A2, Th31;
hence L1 - L2 is Z_Linear_Combination of A by A1, Th27; :: thesis: verum