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 val_inject_antisym v1 v2 : val_inject inject_id v1 v2 -> val_inject inject_id v2 v1 -> v1 = v2.