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MiniZinc

predicate fzn_inverse_reif(array[int] of var int: f,
array[int] of var int: invf,
var bool: b) =
b <-> forall(i in index_set(f), j in index_set(invf)) (
f[i] in index_set(invf) /\
invf[j] in index_set(f) /\
(j == f[i] <-> i == invf[j])
);