 reserve o,o1,o2 for object;
 reserve n for Ordinal;
 reserve R,L for non degenerated comRing;
 reserve b for bag of 1;

theorem Th3:
   for f be sequence of R st f is finite-Support sequence of R holds
   Support f is finite
   proof
     let f be sequence of R;
     assume
A1:  f is finite-Support sequence of R;
     consider n1 be Nat such that
A2:  for i be Nat st i >= n1 holds f.i = 0.R by A1,ALGSEQ_1:def 1;
A3:  for m be Element of NAT st m in Support f holds m < n1
     proof
       let m be Element of NAT;
       assume m in Support f; then
A4:    f.m <> 0.R by POLYNOM1:def 4;
       assume n1 <= m;
       hence contradiction by A4,A2;
     end;
     Support f c= Segm n1 by A3,NAT_1:44;
     hence thesis;
  end;
