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| (* Author: Andreas Lochbihler, ETH Zurich *) | |
| subsection \<open>Ultrafilter\<close> | |
| theory Applicative_Star imports | |
| Applicative | |
| "HOL-Nonstandard_Analysis.StarDef" | |
| begin | |
| applicative star (C, K, W) | |
| for | |
| pure: star_of | |
| ap: Ifun | |
| proof - | |
| show "star_of f \<star> star_of x = star_of (f x)" for f x by(fact Ifun_star_of) | |
| qed(transfer; rule refl)+ | |
| end | |