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Move Bool to live on its own (#118)

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Patrick Stevens
2020-04-18 17:14:39 +01:00
committed by GitHub
parent 264a5e2bd9
commit 84a146f72c
30 changed files with 270 additions and 123 deletions
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Rings/Orders/Total/Lemmas.agda
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@@ -185,6 +185,9 @@ reciprocalPositive a 1/a 0<a ab=1 with totality 0G 1/a
... | inl (inr x) = exFalso (1<0False (<WellDefined (transitive *Commutative ab=1) timesZero' (ringCanMultiplyByPositive 0<a x)))
... | inr x = exFalso (anyComparisonImpliesNontrivial 0<a (transitive (transitive (symmetric timesZero) (*WellDefined reflexive x)) ab=1))
reciprocalPositive' : (a b : A) → .(0<a : 0R < a) → (b * a ∼ 1R) → 0R < b
reciprocalPositive' a 1/a 0<a ab=1 = reciprocalPositive a 1/a 0<a (transitive *Commutative ab=1)
reciprocal<1 : (a b : A) → .(1<a : 1R < a) → (a * b ∼ 1R) → b < 1R
reciprocal<1 a b 0<a ab=1 with totality b 1R
... | inl (inl x) = x