Definition mem_equiv' m1 m2 :=
  (forall x, Mem.perm_order' (access_at m1 x Cur) Readable -> contents_at m1 x = contents_at m2 x) /\
  Mem.perm m1 = Mem.perm m2 /\
  Mem.nextblock m1 = Mem.nextblock m2.Definition mem_lessalloc' m1 m2 :=
  (forall x, Mem.perm_order' (access_at m1 x Cur) Readable -> contents_at m1 x = contents_at m2 x) /\
  Mem.perm m1 = Mem.perm m2 /\
  (Mem.nextblock m1 <= Mem.nextblock m2)%positive.

Lemma mem_lessdef_valid_pointer: forall m1 m2 b z, mem_lessdef m1 m2 -> Mem.valid_pointer m1 b z = true -> Mem.valid_pointer m2 b z = true.