reserve f for Function;
reserve n,k,n1 for Nat;
reserve r,p for Real;
reserve x,y,z for object;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Real_Sequence;

theorem Th5:
  seq is non-zero iff for n holds seq.n<>0
proof
  thus seq is non-zero implies for n holds seq.n<>0
   by ORDINAL1:def 12,Th4;
  assume for n holds seq.n<>0;
  then for x holds x in NAT implies seq.x<>0;
  hence thesis by Th4;
end;
