reserve k,m,n for Nat,
  i1,i2,i3 for Integer,
  e for set;
reserve i,k,m,n,p,x,y for Nat;

theorem Th13:
  0 in k-SD
proof
  defpred P[Nat] means 0 in $1-SD;
A1: for k being Nat st P[k] holds P[k+1]
  proof
    let kk be Nat;
    assume
A2: 0 in kk-SD;
    kk-SD c= (kk+1)-SD by Th9;
    hence thesis by A2;
  end;
A3: P[0] by Th7;
  for k being Nat holds P[k] from NAT_1:sch 2(A3,A1);
  hence thesis;
end;
