istrunc_self_implies_istrunc #2112
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Alizter
reviewed
Oct 10, 2024
| @@ -535,4 +535,13 @@ Proof. | |||
| exact (equiv_iff_hprop_uncurried (iff_contr_hprop A)). | |||
| Defined. | |||
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| (** If a type [A] implies that it is [n.+1]-truncated, then it is [n.+1]-truncated. **) | |||
| Definition istrunc_self_implies_istrunc {n : trunc_index} {A : Type} (H : A -> IsTrunc n.+1 A) | |||
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I would call this istrunc_inhabited_istrunc drawing inspiration from HProp.v.
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@ThomatoTomato looks like you missed this comment. I'll rename it in another PR.
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haha, whoops. I totally forgot to do that, sorry 😅 Thank you Ali
Alizter
approved these changes
Oct 10, 2024
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I found one place it could potentially be useful in |
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My motivation to prove this was originally as a stepping stone to |
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Added this cute little lemma about truncations that might come in handy. All it says is that a map (A -> istrunc n.+1 A) is sufficient to deduce that A is n+1 truncated.
I wasn't so sure what to name it, so feel free to make it fit into your mold.