Definition mequiv P Q := P ⪯ Q /\ Q ⪯ P.
Notation "P ≡𝐦 Q" := (mequiv P Q) (at level 40).
Instance Subrel_mequiv : subrelation mequiv mreducible.
Instance mequiv_proper : Proper (mequiv ==> mequiv ==> iff) mreducible.
Instance Equivalence_mequiv : Equivalence mequiv.

Lemma simple_nontrivial P : simple P -> exists s t, P s /\ ~ P t.
Admitted.