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5 changes: 4 additions & 1 deletion src/Data/Integer/Base.agda
Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,7 @@ module Data.Integer.Base where
open import Algebra.Bundles.Raw
using (RawMagma; RawMonoid; RawGroup; RawNearSemiring; RawSemiring; RawRing)
open import Data.Bool.Base using (Bool; T; true; false)
open import Data.Nat.Base as ℕ using (ℕ; z≤n; s≤s)
open import Data.Nat.Base as ℕ using (ℕ; z≤n; s≤s) hiding (module ℕ)
open import Data.Sign.Base as Sign using (Sign)
open import Level using (0ℓ)
open import Relation.Binary.Core using (Rel)
Expand Down Expand Up @@ -140,6 +140,9 @@ record Negative (i : ℤ) : Set where

-- Instances

open ℕ public
using (nonZero)

instance
pos : ∀ {n} → Positive +[1+ n ]
pos = _
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9 changes: 8 additions & 1 deletion src/Data/Rational/Base.agda
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,9 @@ module Data.Rational.Base where

open import Algebra.Bundles.Raw
open import Data.Bool.Base using (Bool; true; false; if_then_else_)
open import Data.Integer.Base as ℤ using (ℤ; +_; +0; +[1+_]; -[1+_])
open import Data.Integer.Base as ℤ
using (ℤ; +_; +0; +[1+_]; -[1+_])
hiding (module ℤ)
open import Data.Nat.GCD
open import Data.Nat.Coprimality as C
using (Coprime; Bézout-coprime; coprime-/gcd; coprime?; ¬0-coprimeTo-2+)
Expand Down Expand Up @@ -176,6 +178,11 @@ NonPositive p = ℚᵘ.NonPositive (toℚᵘ p)
NonNegative : Pred ℚ 0ℓ
NonNegative p = ℚᵘ.NonNegative (toℚᵘ p)

-- Instances

open ℤ public
using (nonZero; pos; nonNeg; nonPos0; nonPos; neg)

-- Constructors

≢-nonZero : ∀ {p} → p ≢ 0ℚ → NonZero p
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6 changes: 6 additions & 0 deletions src/Data/Rational/Unnormalised/Base.agda
Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@ open import Algebra.Bundles.Raw
open import Data.Bool.Base using (Bool; true; false; if_then_else_)
open import Data.Integer.Base as ℤ
using (ℤ; +_; +0; +[1+_]; -[1+_]; +<+; +≤+)
hiding (module ℤ)
open import Data.Nat.Base as ℕ using (ℕ; zero; suc)
open import Level using (0ℓ)
open import Relation.Nullary.Negation.Core using (¬_; contradiction)
Expand Down Expand Up @@ -149,6 +150,11 @@ NonPositive p = ℤ.NonPositive (↥ p)
NonNegative : Pred ℚᵘ 0ℓ
NonNegative p = ℤ.NonNegative (↥ p)

-- Instances

open ℤ public
using (nonZero; pos; nonNeg; nonPos0; nonPos; neg)

-- Constructors and destructors

-- Note: these could be proved more elegantly using the constructors
Expand Down