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This makes a lot of inductive arguments easier
Now that lower < n is a definitional proposition, we don't need to worry about irrelevance here
This file typechecks, but I suspect that there is an Agda bug lurking
in the shaddows. If you try to typecheck Homotopy.Truncation, a call
to elim! throws the following error:
> Projection _≤_.is-leq is irrelevant.
> Turn on option --irrelevant-projections to use it (unsafe)
> when checking that the expression ._≤_.is-leq (Leq-refl {n}) has
> type Data.Bool.Base.is-true (suc (suc n) ≤? suc (suc n))
This seems to trigger when resolving the 'Inductive' instance using
Inductive-n-Tr, which has the type
> Inductive-n-Tr
> : ∀ {ℓ ℓ' ℓm} {A : Type ℓ} {n} {P : n-Tr A (suc n) → Type ℓ'} ⦃ i : Inductive (∀ x → P (inc x)) ℓm ⦄
> → ⦃ _ : ∀ {x} → H-Level (P x) (suc n) ⦄
> → Inductive (∀ x → P x) ℓm
Moreover, the problematic elim! is eliminating into the universe of
n-Types, which require us to use a hlevel-projection, so I think that
some sequence of events is causing the proof Leq-refl {n} to get
η-expanded to a (bogus) irrelevant projection, which then gets
re-checked by reflection, which then (rightfully) complains.
This seems to solve the issues with Homotopy.Truncation
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Hmmm, looks like we can't remove irrelevancy annotations on some |
plt-amy
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Feb 28, 2026
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bwah i do not want to write a review go away
Co-authored-by: Amélia Liao <me@amelia.how>
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Description
This PR replaces the inductive definitions of
_≤_and_<_onNatandIntwithSoapplied to a decision procedure, and makes the single field ofSoirrelevant. When taken together, these changes make the orderings definitional propositions, which allows us to remove theIrrwrapper onFin.Checklist
Before submitting a merge request, please check the items below:
support/sort-imports.hs(ornix run --experimental-features nix-command -f . sort-imports).If your change affects many files without adding substantial content, and
you don't want your name to appear on those pages (for example, treewide
refactorings or reformattings), start the commit message and PR title with
chore:.