For every type TT and subtype S⊆TS \subseteq T, let f:S→Tf:S \to T be a function from the subtype SS to TT. Given any subtype R⊆TR \subseteq T, the infinitely iterated inverse image is defined as the maximal subtype f −∞(R)⊆Tf^{-\infty}(R) \subseteq T such that the inverse image of f −∞(R)f^{-\infty}(R) under ff is equivalent to f −∞(R)f^{-\infty}(R) itself:
smooth function
iterated inverse image
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