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

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