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Lots of refactoring towards partially-ordered ring R (#109)

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Patrick Stevens
2020-04-10 19:00:57 +01:00
committed by GitHub
parent 1cff95c652
commit 412edaf4c7
19 changed files with 1015 additions and 778 deletions
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8
Fields/CauchyCompletion/Definition.agda
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@@ -42,3 +42,11 @@ CauchyCompletion.converges (injection a) = λ ε 0<e → 0 , λ {m} {n} _ _ →
where
t : (m n : ℕ) → index (constSequence a) m + inverse (index (constSequence a) n) ∼ 0R
t m n = identityOfIndiscernablesLeft _∼_ (identityOfIndiscernablesLeft _∼_ invRight (equalityCommutative (applyEquality (λ i → a + inverse i) (indexAndConst a n)))) (applyEquality (_+ inverse (index (constSequence a) n)) (equalityCommutative (indexAndConst a m)))
-- Some slightly odd things here relating to equality rather than equivalence. Ultimately this is here so we can say Q → R is a genuine injection, not just a setoid one.
private
lemma : {x y : CauchyCompletion} → x ≡ y → CauchyCompletion.elts x ≡ CauchyCompletion.elts y
lemma {x} {.x} refl = refl
CInjection' : Injection injection
CInjection' pr = headInjective (lemma pr)