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Definitions for the reals, classically (#95)

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Patrick Stevens
2020-02-08 13:20:21 +00:00
committed by GitHub
parent d29c7ea681
commit d183b40d11
17 changed files with 786 additions and 15 deletions
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4
Numbers/Naturals/Order/Lemmas.agda
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@@ -84,3 +84,7 @@ cancelInequalityLeft {a} {succ b} {succ c} pr = succPreservesInequality q'
<NProp : {a b : ℕ} → .(a <N b) → a <N b
<NProp {zero} {succ b} a<b = succIsPositive _
<NProp {succ a} {succ b} a<b = succPreservesInequality (<NProp (canRemoveSuccFrom<N a<b))
zeroLeast : {m n : ℕ} → m <N n → 0 <N n
zeroLeast {zero} m<n = m<n
zeroLeast {succ m} {succ n} m<n = le n (applyEquality succ (Semiring.sumZeroRight ℕSemiring n))