 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;

theorem
  for k,n being natural Number holds k < n implies n - 1 is Element of NAT
proof
  let k,n be natural Number;
  assume k < n;
  then k + 1 <= n by Th13;
  then consider j being Nat such that
A1: n = k + 1 + j by Th10;
  n - 1 = k + j by A1;
  hence thesis by ORDINAL1:def 12;
end;
