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

Lemma getThreadCC
{tp} i j
(cnti : containsThread tp i) (cntj : containsThread tp j)
c' (cntj' : containsThread (updThreadC cnti c') j):
getThreadC cntj' = if eq_nat_dec i j then c' else getThreadC cntj.