for L, E being free Z_Module
for I being Subset of L
for J being Subset of E st ModuleStr(# the carrier of L, the addF of L, the ZeroF of L, the lmult of L #) = ModuleStr(# the carrier of E, the addF of E, the ZeroF of E, the lmult of E #) & I = J holds
( I is Basis of L iff J is Basis of E )