theorem Th17:
  seq is non-zero implies seq ^\k is non-zero
proof
  assume
A1: seq is non-zero;
  now
    let n be Nat;
    (seq ^\k).n=seq.(n+k) by NAT_1:def 3;
    hence (seq ^\k).n<>0.S by A1,Th7;
  end;
  hence thesis by Th7;
end;
