@@ -1052,20 +1052,20 @@ private
10521052-- If a decidable predicate P over a finite set is sometimes false,
10531053-- then we can find the smallest value for which this is the case.
10541054
1055- ¬∀⟶ ∃¬-smallest : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
1055+ ¬∀⇒ ∃¬-smallest : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
10561056 ¬ (∀ i → P i) → ∃ λ i → ¬ P i × ((j : Fin′ i) → P (inject j))
1057- ¬∀⟶ ∃¬-smallest zero P P? ¬∀P = contradiction (λ ()) ¬∀P
1058- ¬∀⟶ ∃¬-smallest (suc n) P P? ¬∀P with P? zero
1057+ ¬∀⇒ ∃¬-smallest zero P P? ¬∀P = contradiction (λ ()) ¬∀P
1058+ ¬∀⇒ ∃¬-smallest (suc n) P P? ¬∀P with P? zero
10591059... | false because [¬P₀] = (zero , invert [¬P₀] , λ ())
10601060... | true because [P₀] = map suc (map id (∀-cons (invert [P₀])))
1061- (¬∀⟶ ∃¬-smallest n (P ∘ suc) (P? ∘ suc) (¬∀P ∘ (∀-cons (invert [P₀]))))
1061+ (¬∀⇒ ∃¬-smallest n (P ∘ suc) (P? ∘ suc) (¬∀P ∘ (∀-cons (invert [P₀]))))
10621062
10631063-- When P is a decidable predicate over a finite set the following
10641064-- lemma can be proved.
10651065
1066- ¬∀⟶ ∃¬ : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
1066+ ¬∀⇒ ∃¬ : ∀ n {p} (P : Pred (Fin n) p) → Decidable P →
10671067 ¬ (∀ i → P i) → (∃ λ i → ¬ P i)
1068- ¬∀⟶ ∃¬ n P P? ¬P = map id proj₁ (¬∀⟶ ∃¬-smallest n P P? ¬P)
1068+ ¬∀⇒ ∃¬ n P P? ¬P = map id proj₁ (¬∀⇒ ∃¬-smallest n P P? ¬P)
10691069
10701070------------------------------------------------------------------------
10711071-- Properties of functions to and from Fin
@@ -1277,3 +1277,16 @@ Please use <⇒<′ instead."
12771277"Warning: <′⇒≺ was deprecated in v2.0.
12781278Please use <′⇒< instead."
12791279#-}
1280+
1281+ -- Version 2.4
1282+
1283+ ¬∀⟶∃¬-smallest = ¬∀⇒∃¬-smallest
1284+ {-# WARNING_ON_USAGE ¬∀⟶∃¬-smallest
1285+ "Warning: ¬∀⟶∃¬-smallest was deprecated in v2.4.
1286+ Please use ¬∀⇒∃¬-smallest instead."
1287+ #-}
1288+ ¬∀⟶∃¬ = ¬∀⇒∃¬
1289+ {-# WARNING_ON_USAGE ¬∀⟶∃¬
1290+ "Warning: ¬∀⟶∃¬ was deprecated in v2.4.
1291+ Please use ¬∀⇒∃¬ instead."
1292+ #-}
0 commit comments