Set truncation #13
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Set truncation #13
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ice1000
reviewed
Feb 28, 2020
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| \instance SetTruncTruncated {A : \Type} : Truncated_-1+ 1 (SetTrunc A) | ||
| | isTruncated x y p q => path (\lam i => path (trunc x y p q i)) |
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I wish I can prove this via:
pmap path (path (trunc x y p q))
But it doesn't work, they fail with some type inferences where only one candidates available
| | i, left => x | ||
| | i, right => y |
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Two additional definitional equalities that aren't written in Agda but seem to exist.
ice1000
reviewed
Feb 28, 2020
It's also possible to prove isSet A -> SetTrunc A = A, but I have no time.
| : Path (\lam i => A.2 (p @ i)) b b' ofHLevel_-1+ n \elim p | ||
| | idp => h a b b' |
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We have a much shorter proof rather than in Agda!
ice1000
reviewed
Feb 28, 2020
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This is actually a specialization of |
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As title.