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1 parent a874e6a commit 4c58d51Copy full SHA for 4c58d51
1 file changed
proofs/agda/Ordinal/Buchholz/WellFounded.agda
@@ -57,7 +57,10 @@ rankBT (bpsi μ α) = suc (suc (suc (rankΩ μ)))
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<ᵇ⇒<rankBT (<ᵇ-ψν μ<ν) = s≤s (s≤s (s≤s (<Ω⇒<rankΩ μ<ν)))
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wf-rankBT : WellFounded (_<_ on rankBT)
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-wf-rankBT = WF.InverseImage.wellFounded rankBT NatInd.<-wellFounded
+wf-rankBT x = rank-accessible (NatInd.<-wellFounded (rankBT x))
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+ where
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+ rank-accessible : ∀ {t} → Acc _<_ (rankBT t) → Acc (_<_ on rankBT) t
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+ rank-accessible (acc rs) = acc λ t<x → rank-accessible (rs t<x)
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wf-<ᵇ-rank : WellFounded _<ᵇ_
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wf-<ᵇ-rank = WF.Subrelation.wellFounded <ᵇ⇒<rankBT wf-rankBT
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