reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;
reserve z for Complex;

theorem Th30:
  m < n implies Fermat m < Fermat n
  proof
    assume m < n;
    then 2 |^ m < 2 |^ n by PEPIN:66;
    then 2 |^ (2 |^ m) < 2 |^ (2 |^ n) by PEPIN:66;
    hence thesis by XREAL_1:6;
  end;
