reserve a,b,c,d,e,f for Real,
        k,m for Nat,
        D for non empty set,
        V for non trivial RealLinearSpace,
        u,v,w for Element of V,
        p,q,r for Element of ProjectiveSpace(V);
reserve o,p,q,r,s,t for Point of TOP-REAL 3,
        M for Matrix of 3,F_Real;

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;
