> On 13.09.2016, at 09:45, Peter Lammich <lamm...@in.tum.de> wrote: > > On Di, 2016-09-13 at 00:46 +0100, Lawrence Paulson wrote: >> We have a problem with the ∄ operator, when existential quantifiers >> are nested: >> >> lemma "(∄x. ∃y. P x y) = (~(∃x y. P x y))" >> by (rule refl) > > I do not see a particular problem with this,
Like you I find ∄x. ∃y. P x y clear (albeit weird), but ∄x y. P x y is probably a better way to display the same thing. > lemma "(∄x y. P x y) ⟷ ¬(∃x. ¬(∃y. P x y))" > by (rule refl) That looks like a serious flaw. > lemma "(∃!x y. P x y) ⟷ (∃!x. (∃!y. P x y))" > by (rule refl) Ditto. > We should either forbid multiple variables on those quantifiers, or try > to figure out whether there is a widely-accepted consensus on their > meaning. The best would be to forbid multiple variables for ∃!. For ∄, the situation is more complicated. We can forbid them, or we can interpret a single multi-variable ∄ as ∄∃...∃ (and in the other direction for printing). Jasmin _______________________________________________ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev
