theorem Th34: :: ZMODUL03:34

for p being prime Element of INT.Ring
for V being free Z_Module
for I being Basis of V
for IQ being Subset of (Z_MQ_VectSp (V,p))
for l being Linear_Combination of I st IQ = { (ZMtoMQV (V,p,u)) where u is Vector of V : u in I } holds
ZMtoMQV (V,p,(Sum l)) in Lin IQ