let L1, L2 be Linear_Combination of G; ( ( for h being Element of G holds L1 . h = LG . (h - g) ) & ( for h being Element of G holds L2 . h = LG . (h - g) ) implies L1 = L2 )
assume that
A6:
for h being Element of G holds L1 . h = LG . (h - g)
and
A7:
for h being Element of G holds L2 . h = LG . (h - g)
; L1 = L2
hence
L1 = L2
; verum