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Patrick Stevens
2020-04-11 12:14:03 +01:00
committed by GitHub
parent 412edaf4c7
commit e9aa1bcc05
30 changed files with 424 additions and 98 deletions
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Rings/Definition.agda
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@@ -29,5 +29,7 @@ record Ring {n m} {A : Set n} (S : Setoid {n} {m} A) (_+_ : A → A → A) (_*_
identIsIdent : {a : A} → 1R * a ∼ a
timesZero : {a : A} → a * 0R ∼ 0R
timesZero {a} = symmetric (transitive (transitive (symmetric invLeft) (+WellDefined reflexive (transitive (*WellDefined {a} {a} reflexive (symmetric identRight)) *DistributesOver+))) (transitive +Associative (transitive (+WellDefined invLeft reflexive) identLeft)))
timesZero' : {a : A} → 0R * a ∼ 0R
timesZero' {a} = transitive *Commutative timesZero
*DistributesOver+' : {a b c : A} → (a + b) * c ∼ (a * c) + (b * c)
*DistributesOver+' = transitive *Commutative (transitive *DistributesOver+ (+WellDefined *Commutative *Commutative))