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Lots of rings (#82)

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Patrick Stevens
2019-11-22 19:52:57 +00:00
committed by GitHub
parent b33baa5fb7
commit 660d7aa27c
40 changed files with 1246 additions and 881 deletions
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5
Fields/FieldOfFractions/Multiplication.agda
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@@ -6,7 +6,7 @@ open import Groups.Definition
open import Groups.Lemmas
open import Rings.Definition
open import Rings.Lemmas
open import Rings.IntegralDomains
open import Rings.IntegralDomains.Definition
open import Fields.Fields
open import Functions
open import Setoids.Setoids
@@ -25,8 +25,7 @@ fieldOfFractionsTimes (a ,, (b , b!=0)) (c ,, (d , d!=0)) = (a * c) ,, ((b * d)
open Ring R
ans : ((b * d) ∼ Ring.0R R) → False
ans pr with IntegralDomain.intDom I pr
ans pr | inl x = b!=0 x
ans pr | inr x = d!=0 x
ans pr | f = exFalso (d!=0 (f b!=0))
fieldOfFractionsTimesWellDefined : {a b c d : fieldOfFractionsSet} → (Setoid._∼_ fieldOfFractionsSetoid a c) → (Setoid._∼_ fieldOfFractionsSetoid b d) → (Setoid._∼_ fieldOfFractionsSetoid (fieldOfFractionsTimes a b) (fieldOfFractionsTimes c d))
fieldOfFractionsTimesWellDefined {a ,, (b , _)} {c ,, (d , _)} {e ,, (f , _)} {g ,, (h , _)} af=be ch=dg = need