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
  seq is non-zero implies abs(seq) is non-zero
proof
  assume
A1: seq is non-zero;
  now
    let n;
    seq.n<>0 by A1,Th5;
    then |.seq.n.|<>0 by COMPLEX1:47;
    hence (abs(seq)).n<>0 by Th12;
  end;
  hence thesis by Th5;
end;
