[WIP] Try proving certain_termination

DOES NOT WORK at this point, this is WIP.

wp.v

@@ -233,8 +233,27 @@ Proof.
   - intros p infN. assert (p <= n). omega.
     rewrite (before_n_useless_guard beforeN p H ).
     apply beforeN; trivial.
-  - admit.
-Admitted.
+  - assert (n <= n). omega. rewrite (before_n_useless_guard beforeN n H).
+    destruct mem as [mem0|] eqn:memRel.
+    { simpl in notError. exfalso; apply notError; trivial. }
+    remember (fun n => interp (nth_iterate (ifonly guard body) n) mem)
+      as chain eqn:chainRel.
+    assert (chain (S n) = MemError) as nLastValid.
+    {
+      rewrite chainRel. rewrite memRel. fold MemElem; fold MemElem in atN.
+      rewrite (unfold_one_iter (ifonly guard body) m n).
+      remember (interp (nth_iterate (ifonly guard body) n) (MemElem m))
+        as memN.
+      simpl.
+      destruct memN; trivial.
+      simpl in atN. unfold expr_neg in atN.
+      destruct (guard m0); simpl; trivial.
+      * exfalso. apply atN. congruence.
+    assert (forall n, chain n cpo<= chain (S n)) as incrChainRel.
+    * intros n0. rewrite chainRel. unfold cpo_leq.
+      destruct (n0 <=? n).
+    assert (find_lub_correct
+Qed.
 
 (***** Validite, prouvabilite pour Hoare *************************************)