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Polynomial ring (#76)

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Patrick Stevens
2019-11-17 17:37:10 +00:00
committed by GitHub
parent c55dd5f63e
commit 8377c23613
23 changed files with 984 additions and 341 deletions
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4
Numbers/Integers/Order.agda
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@@ -4,6 +4,7 @@ open import LogicalFormulae
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Integers.Definition
open import Numbers.Integers.RingStructure.Ring
open import Numbers.Integers.Addition
open import Numbers.Integers.Multiplication
open import Semirings.Definition
@@ -30,9 +31,6 @@ lessLemma (succ a) x pr = lessLemma a x q
q : succ x +N a ≡ a
q rewrite Semiring.commutative ℕSemiring a (succ x) | Semiring.commutative ℕSemiring x a | Semiring.commutative ℕSemiring (succ a) x = succInjective pr
nonnegInjective : {a b : ℕ} → (nonneg a ≡ nonneg b) → (a ≡ b)
nonnegInjective {a} {.a} refl = refl
irreflexive : (x : ℤ) → x <Z x → False
irreflexive (nonneg x) record { x = y ; proof = proof } = lessLemma x y (nonnegInjective proof)
irreflexive (negSucc a) record { x = x ; proof = proof } = naughtE (equalityCommutative q)