section‹Lifting theorems onto filters› theory Eventuallize imports Complex_Main begin
text‹ The following attribute and ML function lift a given theorem of the form 🍋‹∀x. A x ⟶ B x ⟶ C x› to 🍋‹eventually A F ==> eventually B F ==> eventually C F›. ›
ML ‹ signature EVENTUALLIZE = sig val eventuallize : Proof.context -> thm -> int option -> thm end structure Eventuallize : EVENTUALLIZE = struct fun dest_All (Const (🍋‹HOL.All›, _) $ Abs (x, T, t)) = (x, T, t) | dest_All (Const (🍋‹HOL.All›, T) $ f) = ("x", T |> dest_funT |> fst |> dest_funT |> fst, f $ Bound 0) | dest_All t = raise TERM ("dest_All", [t]) fun strip_imp (🍋‹(⟶)›$ a $ b) = apfst (cons a) (strip_imp b) | strip_imp t = ([], t) fun eventuallize ctxt thm n = let fun err n = raise THM ("Invalid index in eventuallize: " ^ Int.toString n, 0, [thm]) val n_max = thm |> Thm.concl_of |> HOLogic.dest_Trueprop |> dest_All |> #3 |> strip_imp |> fst |> length val _ = case n of NONE => () | SOME n => if n >= 0 andalso n 🚫n_max then () else err n val n = case n of SOME n => n | NONE => n_max fun conv n = if n 🚫 then Conv.all_conv else Conv.arg_conv (conv (n - 1)) then_conv Conv.rewr_conv @{thm eq_reflection[OF imp_conjL [symmetric]]} val conv = Conv.arg_conv (Conv.binder_conv (K (conv n)) ctxt) val thm' = Conv.fconv_rule conv thm fun go n = if n 🚫 then @{thm _} else @{thm eventually_conj} OF [@{thm _}, go (n - 1)] in @{thm eventually_rev_mp[OF _ always_eventually]} OF [go n, thm'] end end ›
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