(** *** 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 gsoFP :
forall tpc i j f' (fp : fpool tpc) (cnti: containsThread tpc i)
(cntj: containsThread tpc j) (Hneq: i <> j),
(updateFP cnti fp f') j cntj = fp j cntj.