Arguments InA {A}{eqA} x _.
Arguments AMap.In {elt} x m.

Lemma add_updateC_comm:
forall tp i vf arg pmap c'
(cnti: containsThread tp i)
(cnti': containsThread (addThread tp vf arg pmap) i),
addThread (updThreadC cnti c') vf arg pmap =
updThreadC cnti' c'.