 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 < k + n iff 1 <= n
proof
  let k,n be natural Number;
  thus k < k + n implies 1 <= n
  proof
    assume
A1: k < k + n;
    assume not 1 <= n;
    then n = 0 by Th14;
    hence thesis by A1;
  end;
  assume 1 <= n;
  hence thesis by Th16;
end;
