Instance mreducible_preorder : PreOrder mreducible.

(* Specifications: *)
Lemma mreducible_ext P Q P' Q' :
(forall s, P s <-> P' s) -> (forall s, Q s <-> Q' s) -> P ⪯ Q -> P' ⪯ Q'.
Lemma mreducible_comp P Q :
P ⪯ Q -> (fun s => ~ P s) ⪯ (fun s => ~ Q s).
Lemma mreducible_comp_conv :
(forall P Q, (fun s => ~ P s) ⪯ (fun s => ~ Q s) -> P ⪯ Q) ->
Markov_Eva.
Lemma mreducible_dec P Q :
decidable Q -> P ⪯ Q -> decidable P.
Lemma mreducible_red P Q s t :
Q s -> ~ Q t -> decidable P -> P ⪯ Q.
Lemma mreducible_recognisable P Q :
recognisable Q -> P ⪯ Q -> recognisable P.
Lemma mreducible_full P :
P ⪯ (fun s => True) <-> (forall s, P s).
Lemma mreducible_empty P :
P ⪯ (fun s => False) <-> (forall s, ~ P s).
Lemma eva_red :
(fun s => eva (s (tenc s))) ⪯ eva.
Lemma recognisable_iff P :
recognisable P <-> P ⪯ eva.
Lemma preceq_lub P Q : exists R,
P ⪯ R /\ Q ⪯ R /\ forall R', P ⪯ R' -> Q ⪯ R' -> R ⪯ R'.