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chore: simplify the connection between HasFresh and Infinite #303

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fmontesi merged 1 commit into from
Jan 30, 2026
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chore: simplify the connection between HasFresh and Infinite #303

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16 changes: 9 additions & 7 deletions Cslib/Foundations/Data/HasFresh.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -132,15 +132,17 @@ end

export HasFresh (fresh fresh_notMem fresh_exists)

set_option linter.unusedFintypeInType false in
lemma HasFresh.not_of_finite (α : Type u) [Fintype α] : IsEmpty (HasFresh α) :=
⟨fun f ↦ (f.fresh_notMem .univ).elim (Finset.mem_univ _)⟩
/-- `HasFresh α` implies a computably infinite type. -/
instance HasFresh.to_infinite (α : Type u) [HasFresh α] : Infinite α := by
apply Infinite.of_not_fintype
rintro ⟨elems, _⟩
grind [fresh_notMem elems]

/-- All infinite types have an associated (at least noncomputable) fresh function.
This, in conjunction with `HasFresh.not_of_finite`, characterizes `HasFresh`. -/
noncomputable def HasFresh.of_infinite (α : Type u) [Infinite α] : HasFresh α where
fresh s := s.finite_toSet.infinite_compl.nonempty.choose
fresh_notMem s := s.finite_toSet.infinite_compl.nonempty.choose_spec
This, in conjunction with `HasFresh.to_infinite`, characterizes `HasFresh`. -/
noncomputable instance HasFresh.of_infinite (α : Type u) [Infinite α] : HasFresh α where
fresh s := Infinite.exists_notMem_finset s |>.choose
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@ctchou ctchou Jan 30, 2026

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I really don't know what the preferred style is: should there be a space between |> and .?

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@chenson2018 chenson2018 Jan 30, 2026

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These are semantically different:

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@ctchou ctchou Jan 30, 2026

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Good to know that. Thanks!

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@ctchou ctchou Jan 30, 2026

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In this case, I wonder if (Infinite.exists_notMem_finset s).choose is actually clearer.

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@chenson2018 chenson2018 Jan 30, 2026

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I am fairly ambivalent, but I think this is a common enough core syntax to not be considered obfuscatory. I wrote it without thinking, not as a golfing attempt.

fresh_notMem s := by grind

open Finset in
/-- Construct a fresh element from an embedding of `ℕ` using `Nat.find`. -/
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