(** *** Lemmas about renaming pools [fpool]*)
Definition updateFP {tpc i} (cnti: containsThread tpc i)
(fp: fpool tpc) (f' : memren) :=
fun j cntj => if i == j then f' else fp j cntj.

Lemma gssFP :
forall tpc i f' (fp : fpool tpc) (cnti: containsThread tpc i),
(updateFP cnti fp f') i cnti = f'.