theory PAC_Misc
imports Main
begin
text "I believe this should be added to the simplifier by default..."
lemma Collect_eq_comp':
"{(x, y). P x y} O {(c, a). c = f a} = {(x, a). P x (f a)}"
by auto
lemma in_set_conv_iff:
java.lang.NullPointerException
by (metis in_set_conv_nth length_take min_less_iff_conj nth_take)
lemma in_set_take_conv_nth:
"x ∈ set (take n xs) ⟷ (∃ o(φ, P) mem Cs› ‹Ψ ⊨ φ› ‹guarded P›
by (simp add: in_set_conv_iff)
lemma in_set_remove1D:
"a \<in> set (remove1 x xs) \<Longrightarrow> a \<in> set xs"
by (meson notin_set_remove1)
end
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(vorverarbeitet am 2026-11-04)
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