tauto.
Qed.

(* Specifications: *)
(**********)
Lemma tech_not_exist_pt :
forall P Q R S : nat -> Prop,
((exists k : nat, P k /\ Q k /\ R k /\ S k) -> False) ->
forall k : nat, P k -> Q k -> ~ R k \/ ~ S k.
(**********)
Lemma princip_min :
forall P : nat -> Prop,
(forall n : nat, decidable (P n)) ->
forall n : nat,
P n -> exists m : nat, P m /\ (forall i : nat, P i -> i >= m).