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[ deprecate ] names for deMorgan lemmas in Data.Fin.Properties #2837

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Oct 26, 2025
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[ deprecate ] names for deMorgan lemmas in Data.Fin.Properties #2837

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b3265a6
deprecate: names for deMorgan lemmas
jamesmckinna Oct 9, 2025
d0bc9f0
Merge branch 'master' into deMorgan-Fin
jamesmckinna Oct 26, 2025
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6 changes: 6 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -46,6 +46,12 @@ Deprecated names
interchange ↦ medial
```

* In `Data.Fin.Properties`:
```agda
¬∀⟶∃¬-smallest ↦ ¬∀⇒∃¬-smallest
¬∀⟶∃¬- ↦ ¬∀⇒∃¬
```

New modules
-----------

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25 changes: 19 additions & 6 deletions src/Data/Fin/Properties.agda
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Expand Up @@ -1052,20 +1052,20 @@ private
-- If a decidable predicate P over a finite set is sometimes false,
-- then we can find the smallest value for which this is the case.

¬∀⟶∃¬-smallest : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
¬∀⇒∃¬-smallest : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
¬ (∀ i → P i) → ∃ λ i → ¬ P i × ((j : Fin′ i) → P (inject j))
¬∀⟶∃¬-smallest zero P P? ¬∀P = contradiction (λ()) ¬∀P
¬∀⟶∃¬-smallest (suc n) P P? ¬∀P with P? zero
¬∀⇒∃¬-smallest zero P P? ¬∀P = contradiction (λ()) ¬∀P
¬∀⇒∃¬-smallest (suc n) P P? ¬∀P with P? zero
... | false because [¬P₀] = (zero , invert [¬P₀] , λ ())
... | true because [P₀] = map suc (map id (∀-cons (invert [P₀])))
(¬∀⟶∃¬-smallest n (P ∘ suc) (P? ∘ suc) (¬∀P ∘ (∀-cons (invert [P₀]))))
(¬∀⇒∃¬-smallest n (P ∘ suc) (P? ∘ suc) (¬∀P ∘ (∀-cons (invert [P₀]))))

-- When P is a decidable predicate over a finite set the following
-- lemma can be proved.

¬∀⟶∃¬ : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
¬∀⇒∃¬ : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
¬ (∀ i → P i) → (∃ λ i → ¬ P i)
¬∀⟶∃¬ n P P? ¬P = map id proj₁ (¬∀⟶∃¬-smallest n P P? ¬P)
¬∀⇒∃¬ n P P? ¬P = map id proj₁ (¬∀⇒∃¬-smallest n P P? ¬P)

------------------------------------------------------------------------
-- Properties of functions to and from Fin
Expand Down Expand Up @@ -1277,3 +1277,16 @@ Please use <⇒<′ instead."
"Warning: <′⇒≺ was deprecated in v2.0.
Please use <′⇒< instead."
#-}

-- Version 2.4

¬∀⟶∃¬-smallest = ¬∀⇒∃¬-smallest
{-# WARNING_ON_USAGE ¬∀⟶∃¬-smallest
"Warning: ¬∀⟶∃¬-smallest was deprecated in v2.4.
Please use ¬∀⇒∃¬-smallest instead."
#-}
¬∀⟶∃¬ = ¬∀⇒∃¬
{-# WARNING_ON_USAGE ¬∀⟶∃¬
"Warning: ¬∀⟶∃¬ was deprecated in v2.4.
Please use ¬∀⇒∃¬ instead."
#-}