The library has been tested using Agda 2.6.4 and 2.6.4.1.
- In
Data.Nat.Divisibility.Core
:*-pres-∣ ↦ Data.Nat.Divisibility.*-pres-∣
Function.Relation.Binary.Equality
and a convenient infix versionsetoid : Setoid a₁ a₂ → Setoid b₁ b₂ → Setoid _ _
_⇨_ = setoid
-
In
Data.Fin.Properties
:nonZeroIndex : Fin n → ℕ.NonZero n
-
In
Data.List.Relation.Unary.All.Properties
:All-catMaybes⁺ : All (Maybe.All P) xs → All P (catMaybes xs) Any-catMaybes⁺ : All (Maybe.Any P) xs → All P (catMaybes xs)
-
In
Data.List.Relation.Unary.AllPairs.Properties
:catMaybes⁺ : AllPairs (Pointwise R) xs → AllPairs R (catMaybes xs) tabulate⁺-< : (i < j → R (f i) (f j)) → AllPairs R (tabulate f)
-
In
Data.Maybe.Relation.Binary.Pointwise
:pointwise⊆any : Pointwise R (just x) ⊆ Any (R x)
-
In
Data.Nat.Divisibility
:quotient≢0 : m ∣ n → .{{NonZero n}} → NonZero quotient m|n⇒n≡quotient*m : m ∣ n → n ≡ quotient * m m|n⇒n≡m*quotient : m ∣ n → n ≡ m * quotient quotient-∣ : m ∣ n → quotient ∣ n quotient>1 : m ∣ n → m < n → 1 < quotient quotient-< : m ∣ n → .{{NonTrivial m}} → .{{NonZero n}} → quotient < n n/m≡quotient : m ∣ n → .{{_ : NonZero m}} → n / m ≡ quotient m/n≡0⇒m<n : .{{_ : NonZero n}} → m / n ≡ 0 → m < n m/n≢0⇒n≤m : .{{_ : NonZero n}} → m / n ≢ 0 → n ≤ m nonZeroDivisor : DivMod dividend divisor → NonZero divisor
-
Added new proofs in
Data.Nat.Properties
:m≤n+o⇒m∸n≤o : ∀ m n {o} → m ≤ n + o → m ∸ n ≤ o m<n+o⇒m∸n<o : ∀ m n {o} → .{{NonZero o}} → m < n + o → m ∸ n < o pred-cancel-≤ : pred m ≤ pred n → (m ≡ 1 × n ≡ 0) ⊎ m ≤ n pred-cancel-< : pred m < pred n → m < n pred-injective : .{{NonZero m}} → .{{NonZero n}} → pred m ≡ pred n → m ≡ n pred-cancel-≡ : pred m ≡ pred n → ((m ≡ 0 × n ≡ 1) ⊎ (m ≡ 1 × n ≡ 0)) ⊎ m ≡ n
-
Added new functions in
Data.String.Base
:map : (Char → Char) → String → String