theorem Th34:
  Mx2Tran M1 = Mx2Tran M2 implies M1 = M2
proof
  assume that
   A1: Mx2Tran M1=Mx2Tran M2;
  set Vn=n-VectSp_over F_Real,Vm=m-VectSp_over F_Real;
  reconsider Bn=MX2FinS 1.(F_Real,n) as OrdBasis of Vn by MATRLIN2:45;
  reconsider Bm=MX2FinS 1.(F_Real,m) as OrdBasis of Vm by MATRLIN2:45;
A2: len Bm=m by Th19;
  len Bn=n by Th19;
  then reconsider A1=M1,B1=M2 as Matrix of len Bn,len Bm,F_Real by A2;
  A3: Mx2Tran(A1,Bn,Bm)=Mx2Tran M1 by Th20
   .=Mx2Tran(B1,Bn,Bm) by A1,Th20;
  thus M1=AutMt(Mx2Tran(A1,Bn,Bm),Bn,Bm) by MATRLIN2:36
   .=M2 by A3,MATRLIN2:36;
end;
