theorem Th32:
  for M being Matrix of k,m,F_Real holds
  Mx2Tran M is Function of RLSp2RVSp(TOP-REAL k),RLSp2RVSp(TOP-REAL m)
  proof
    let M be Matrix of k,m,F_Real;
    RLSp2RVSp(TOP-REAL k) =
     ModuleStr (# the carrier of TOP-REAL k, the addF of TOP-REAL k,
      the ZeroF of TOP-REAL k, MultF_Real*(TOP-REAL k) #) &
    RLSp2RVSp(TOP-REAL m) =
     ModuleStr (# the carrier of TOP-REAL m, the addF of TOP-REAL m,
      the ZeroF of TOP-REAL m, MultF_Real*(TOP-REAL m) #) by DUALSP01:def 2;
    hence thesis;
  end;
