Variables (A : {set aT}) (S T : {set rT}).
Hypotheses (AactS : [acts A, on S | to]) (AactT : [acts A, on T | to]).

Lemma reindex_acts A a F : [acts A, on S | to] -> a \in A ->
\big[op/idx]_(i in S) F i = \big[op/idx]_(i in S) F (to i a).