let V be non empty CLSStruct ; :: thesis: for A being Subset of V
for L1, L2 being C_Linear_Combination of V st L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of A holds
L1 - L2 is C_Linear_Combination of A
let A be Subset of V; :: thesis: for L1, L2 being C_Linear_Combination of V st L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of A holds
L1 - L2 is C_Linear_Combination of A
let L1, L2 be C_Linear_Combination of V; :: thesis: ( L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of A implies L1 - L2 is C_Linear_Combination of A )
assume A1: ( L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of A ) ; :: thesis: L1 - L2 is C_Linear_Combination of A
then - L2 is C_Linear_Combination of A by Th67;
hence L1 - L2 is C_Linear_Combination of A by A1, Th59; :: thesis: verum