Definition MemE := Mem_Simpl.

(* Specifications: *)
Lemma Mem_Mem (p : pT) : (Mem (Mem p) = Mem p) * (Mem [Mem p] = Mem p).
Lemma EqPredType_refl (r : pT) : EqPredType r r.
Lemma SubPredType_refl (r : pT) : SubPredType r r.
Lemma EqPredType_sym (r1 r2 : pT) : EqPredType r1 r2 -> EqPredType r2 r1.
Lemma EqPredType_trans' (r1 r2 r3 : pT) : EqPredType r1 r2 -> EqPredType r2 r3 -> EqPredType r1 r3.
Lemma SubPredType_trans' (r1 r2 r3 : pT) : SubPredType r1 r2 -> SubPredType r2 r3 -> SubPredType r1 r3.