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(* Exercise 5.16 *)
Definition my_le (n p : nat) :=
forall P : nat -> Prop, P n -> (forall q : nat, P q -> P (S q)) -> P p.
Lemma my_le_n : forall n : nat, my_le n n.
Proof.
unfold my_le.
intros n P H H0.
assumption.
Qed.
Lemma my_le_S : forall n p : nat, my_le n p -> my_le n (S p).
intros n p H P H0 H1.
apply H1.
apply H.
intros q H2.
Lemma my_le_le : forall n p : nat, my_le n p -> n <= p.
intros n p H.
pattern p.
apply le_n.
intros q H0.
apply le_S.
