
theorem
  ModuleStr(# the carrier of INT.Ring, the addF of INT.Ring,
  the ZeroF of INT.Ring, Int-mult-left(INT.Ring) #)
  is Submodule of Rat-Module
  proof
    set W = ModuleStr(# the carrier of INT.Ring, the addF of INT.Ring,
    the ZeroF of INT.Ring, Int-mult-left(INT.Ring) #);
    set V = Rat-Module;
    G1: W is Z_Module by ZMODUL01:164;
    P2: 0.W = 0.V;
    (the addF of V) || the carrier of W
    = the addF of W by LMLT12,GAUSSINT:13,NUMBERS:14,RELAT_1:74,ZFMISC_1:96;
    hence thesis by G1,P2,LMLT11,NUMBERS:14,VECTSP_4:def 2;
  end;
