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Rename some confusing fields (#51)

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Patrick Stevens
2019-10-13 09:31:54 +01:00
committed by GitHub
parent 96d15c6017
commit 959071214e
21 changed files with 441 additions and 441 deletions
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14
Numbers/Integers/Addition.agda
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@@ -76,14 +76,14 @@ additiveInverse (nonneg (succ x)) = negSucc x
additiveInverse (negSucc x) = nonneg (succ x)
ℤGroup : Group (reflSetoid ℤ) (_+Z_)
Group.wellDefined ℤGroup refl refl = refl
Group.identity ℤGroup = nonneg 0
Group.+WellDefined ℤGroup refl refl = refl
Group.0G ℤGroup = nonneg 0
Group.inverse ℤGroup = additiveInverse
Group.multAssoc ℤGroup {a} {b} {c} = +ZAssociative a b c
Group.multIdentRight ℤGroup {nonneg zero} = refl
Group.multIdentRight ℤGroup {nonneg (succ x)} = applyEquality (λ i → nonneg (succ i)) (Semiring.commutative ℕSemiring x 0)
Group.multIdentRight ℤGroup {negSucc x} = refl
Group.multIdentLeft ℤGroup = refl
Group.+Associative ℤGroup {a} {b} {c} = +ZAssociative a b c
Group.identRight ℤGroup {nonneg zero} = refl
Group.identRight ℤGroup {nonneg (succ x)} = applyEquality (λ i → nonneg (succ i)) (Semiring.commutative ℕSemiring x 0)
Group.identRight ℤGroup {negSucc x} = refl
Group.identLeft ℤGroup = refl
Group.invLeft ℤGroup {nonneg zero} = refl
Group.invLeft ℤGroup {nonneg (succ x)} = additiveInverseExists x
Group.invLeft ℤGroup {negSucc x} = transitivity (+ZCommutative (nonneg (succ x)) (negSucc x)) (additiveInverseExists x)