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

Lemma updThread_updThreadC_comm :
forall tp i j c pmap' c'
(Hneq: i <> j)
(cnti : containsThread tp i)
(cntj : containsThread tp j)
(cnti': containsThread (updThread cntj c' pmap') i)
(cntj': containsThread (updThreadC cnti c) j),
updThreadC cnti' c = updThread cntj' c' pmap'.