theorem Th6: :: MATRLIN:6

for K being Field
for V being VectSp of K
for KL1, KL2, KL3 being Linear_Combination of V
for X being Subset of V st X is linearly-independent & Carrier KL1 c= X & Carrier KL2 c= X & Carrier KL3 c= X & Sum KL1 = (Sum KL2) + (Sum KL3) holds
KL1 = KL2 + KL3