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Merged
felixwellen
merged 2 commits into
agda:master
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LorenzoMolena:StrictOrderEquationalReasoning
May 19, 2025
Merged
Strict order equational reasoning #1203
felixwellen
merged 2 commits into
agda:master
from
LorenzoMolena:StrictOrderEquationalReasoning
May 19, 2025
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Co-authored-by: Ettore Forigo <ettore.forigo@gmail.com>
marcinjangrzybowski
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Jun 26, 2025
commit d08dabfacb486fb77a2ded077a3f0593968412e8 Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 22:32:26 2025 +0200 works commit 74b6ee0df2aaba26be3f09f81b2020470b27cc44 Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 22:29:59 2025 +0200 gi commit f89d4d7f172ae7da24a385efdd783209a5b2bdea Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 22:29:15 2025 +0200 gi commit 3528c1128f48573748c240b3b5d3ea27fee5e0e5 Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 20:04:00 2025 +0200 cleanup commit 4028c0010c1f0f48f54577ce418185648b2b9902 Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 20:02:46 2025 +0200 cleanup commit 02f1aa892a739e61be52f2a609d0bd5891133639 Merge: 07914eea ac62dd4 Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 19:09:38 2025 +0200 pre-merge commit 07914eeae43b77109983039e6d2e6c67fbae3f2f Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jun 26 18:59:53 2025 +0200 integration done commit ac62dd4 Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Wed Jun 25 17:16:13 2025 +0530 Add Rezk Completion by HIT (agda#1188) * Add Rezk Completion by HIT * Update Construction.agda * Removed trailing whitespaces * Remove trailing whitespace * Replace HIT with GroupoidQuotient * shorter proof of `inc-surj` * fix whitespace * Forgot to import GroupoidQuotients * add implicit argument commit b15ec4e Author: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Date: Tue Jun 24 06:45:56 2025 +0200 wip commit 55479ef Author: Marcin Jan Turek-Grzybowski <marcin@Marcins-MacBook-Pro.local> Date: Wed May 28 16:00:42 2025 +0200 wip - dirty commit ecf1bbb Author: Laine Taffin Altman <alexanderaltman@me.com> Date: Fri May 23 03:17:16 2025 -0700 Fix makefile race condition (agda#1210) If you use `make -j gen-everythings listings`, currently there is a near-certainty that the `listings` task will fail because the Everythings modules haven't been generated yet. This PR enforces the dependency. commit 43183c8 Author: michael <1700346+mzhang28@users.noreply.github.com> Date: Thu May 22 17:01:37 2025 -0500 Five lemma (agda#1166) * exact sequences * complete five proof * make five safe * fix newline * exactness over a successor structure * working again * fix whitespace... * clean up, just five * clean up * make implicit + rename isExact so the names are more descriptive * fix whitespace commit 63d187d Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Tue May 20 22:52:24 2025 +0530 Formalize Theorem 7.2.2 in the HoTT Book (agda#1180) * Formalize Theorem 7.2.2 in the HoTT Book * move Theorem 7.2.2 to Cubical.Relation.Binary.Properties * Remove a few extra spaces This is not really necessary but it looks better commit 06e62f4 Author: michael <1700346+mzhang28@users.noreply.github.com> Date: Tue May 20 07:24:54 2025 -0500 Composition of left module homomorphisms (agda#1176) * implement composition of left module homomorphisms * pull out to top level * fix whitespace commit 78203ee Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Mon May 19 21:41:29 2025 +0530 Remove duplicated lemma (agda#1189) * Remove duplicated lemma agda#1017 * Insert brackets commit 2738401 Author: LorenzoMolena <164308953+LorenzoMolena@users.noreply.github.com> Date: Mon May 19 17:52:30 2025 +0200 Strict order equational reasoning (agda#1203) * Add QuosetReasoning.agda Co-authored-by: Ettore Forigo <ettore.forigo@gmail.com> * add missing `no-eta-equality` in SubRelation, make SubRelation instance private --------- Co-authored-by: Ettore Forigo <ettore.forigo@gmail.com> commit 69b70a2 Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Mon May 19 21:19:57 2025 +0530 Add inducedFun for EM1 (agda#1208) * Add files via upload * Delete Base.agda No idea what this file is doing here * Delete Properties.agda Must have accidentally put this here when I was editing dagger-cat * Add inducedFun for EM1 commit 22458b7 Author: LeeeeT <me@LeeeeT.dev> Date: Mon May 19 18:46:33 2025 +0300 Add missing minus symbol (agda#1207) commit 3291fc1 Author: Felix Cherubini <felix.cherubini@posteo.de> Date: Mon May 19 17:24:35 2025 +0200 Release for agda 2.7 (agda#1206) * test new ci script * fix * use fix-whitespace action * blindly try stuff * blindly try stuff * blindly try stuff * untabify... * Revert "blindly try stuff" This reverts commit 6fe71f3. # Conflicts: # .github/workflows/ci-ubuntu.yml * use fix-whitespace action * whitespace * whitespace * fix * fix * fix * fix * Fix path of fix-whitespace * Remove unnecessary step to generate user-manual.pdf * Bump base in cubical-utils.cabal * bump version number everywhere, update README and RELEASE * trailing newline needed? * update flake --------- Co-authored-by: Andreas Abel <andreas.abel@ifi.lmu.de> Co-authored-by: Naïm Favier <n@monade.li> commit eef2ed6 Author: Marcin Jan Turek-Grzybowski <marcin@Marcins-MacBook-Pro.local> Date: Thu May 15 07:17:58 2025 +0200 wip commit 71f32f0 Author: Andreas Abel <andreas.abel@ifi.lmu.de> Date: Fri May 9 21:51:25 2025 +0200 Prep for Agda 2.8.0: remove some spurious `private` commit d5b7bce Author: Marcin Grzybowski <marcinjangrzybowski@gmail.com> Date: Mon Apr 21 20:46:48 2025 +0200 sync commit 35d2919 Merge: 385066b cb0510c Author: Evan Cavallo <evanc@chalmers.se> Date: Fri Mar 21 06:08:36 2025 +0100 Merge pull request agda#1157 from Trebor-Huang/devalapurkar-haine Devalapurkar & Haine commit cb0510c Author: ecavallo <evancavallo@gmail.com> Date: Thu Mar 20 18:40:56 2025 +0100 cosmetic changes commit 52cf2a1 Author: ecavallo <evancavallo@gmail.com> Date: Thu Mar 20 18:40:42 2025 +0100 more informative type signatures commit 01c36f4 Author: ecavallo <evancavallo@gmail.com> Date: Thu Mar 20 18:40:23 2025 +0100 prefer copattern matching to record syntax commit fa0eba6 Author: ecavallo <evancavallo@gmail.com> Date: Thu Mar 20 13:59:26 2025 +0100 make pushout to wedge equivalence opaque commit 4155afd Merge: 01fa420 385066b Author: ecavallo <evancavallo@gmail.com> Date: Tue Mar 18 14:01:34 2025 +0100 Merge branch 'master' into devalapurkar-haine commit 385066b Author: Loïc Pujet <38562414+loic-p@users.noreply.github.com> Date: Tue Mar 4 16:53:03 2025 +0100 Reduced homology of CW complexes (agda#1175) * Reduced homology of CW complexes * explicit description of the augmentation map commit 90c3244 Author: Marcin Grzybowski <marcinjangrzybowski@gmail.com> Date: Fri Feb 14 16:53:06 2025 +0100 wip commit e8ff0c1 Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Fri Feb 14 21:06:39 2025 +0530 Move `factorial` from `Cubical.Data.Fin.LehmerCode` to `Cubical.Data.Nat.Properties` (agda#1184) * Update LehmerCode.agda * Update Properties.agda add `factorial` here * Update LehmerCode.agda made it export `factorial` so nothing else in the library that depends on `factorial` being exported breaks * Removed dependency on LehmerCode exporting `factorial` * Removed dependency on LehmerCode exporting `factorial` * Removed dependency on LehmerCode exporting `factorial` * Remove the public export of `factorial` from LehmerCode.agda commit 3d5bb7d Author: Brad Dragun <35275808+LuuBluum@users.noreply.github.com> Date: Tue Feb 11 23:02:11 2025 -0700 Fix missed rename of StrictPoset to Quoset (agda#1185) commit c16edad Author: anshwad10 <109362320+anshwad10@users.noreply.github.com> Date: Sat Feb 8 21:32:52 2025 +0530 Remove duplicated factorial function (agda#1183) `_!` is defined in `Cubical.Data.Nat.Properties`, `factorial` is defined in `Cubical.Data.Fin.LehmerCode`, and they both have identical definitions. commit f717d46 Author: Brad Dragun <35275808+LuuBluum@users.noreply.github.com> Date: Fri Feb 7 09:27:29 2025 -0700 Basic Order Theory (agda#1154) * Add inverses to monoids/comm monoids * Add meets and joins to order properties * Rewrite isConnected and rename isStronglyConnected * Decidable total and linear orders imply discrete * Remove discrete requirement * Move decidable->discrete from toset to poset * Define binary meets/joins and prove properties * The negation of a linear order is a poset * Define bounds on a poset * Mild refactoring Rename preorder to proset; rename strict poset to quoset (quasiorder) and add strict orders as quasiorders with weak linearity * Remove unnecessary constructors * Define tight relations * Reintroduce constructors * Lattice basics * Distributive lattices * Replace compEquiv usages * Total orders are distributive pseudolattices * Add pseudolattice assumption to make more useful * Mappings on posets * Downsets and upsets are preserved * Defined complete lattices * Duals and closures * Embeddings form a complete lattice * Dual closures * Bicomplete subsets * Poset equivalences * Galois connections * Fix typo * Fix whitespace * Fix build failures * Move PosetDownset to where principalDownsets are * Fix build failures * Split mappings and subsets * Fix whitespace * Proofs regarding residuals and involutions * Cleaner proof commit f344485 Author: Marcin Grzybowski <marcinjangrzybowski@gmail.com> Date: Thu Jan 30 15:55:08 2025 +0100 wip commit 01fa420 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 22:16:54 2024 +0800 safe flags commit 54a2b1f Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 21:42:05 2024 +0800 Fix whitespace commit a181af8 Merge: f0d49bc 53e400e Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 21:36:50 2024 +0800 Merge remote-tracking branch 'origin/master' into devalapurkar-haine commit f0d49bc Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 21:27:40 2024 +0800 James commit d99570a Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 21:10:57 2024 +0800 Hilton–Milnor commit c983de7 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 20:36:36 2024 +0800 Splitting of loopspace commit 08a56c4 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 20:21:45 2024 +0800 Oddly specific sigma lemma commit 51fa7d0 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Sep 19 20:12:35 2024 +0800 Remove my version in favor of the other commit dee0c56 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Sun Aug 18 00:08:50 2024 +0800 extend commutative squares commit 98bbb7a Author: Trebor-Huang <treborhuang@foxmail.com> Date: Sun Aug 18 00:08:43 2024 +0800 tweak commit a4b23dd Author: Trebor-Huang <treborhuang@foxmail.com> Date: Thu Aug 15 17:45:42 2024 +0800 Rename commit dac0c0e Author: Trebor-Huang <treborhuang@foxmail.com> Date: Tue Aug 13 02:07:32 2024 +0800 Pushout using Unit* commit f9fc7e3 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 13:50:15 2024 +0800 Use PushoutSquare instead commit 72a7557 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 03:58:36 2024 +0800 Universes commit 9d50340 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 03:18:06 2024 +0800 Susp (X∙ ⋀ Y∙) ≡ join X Y commit 4bc6517 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 02:51:38 2024 +0800 Pushout⋁≃Unit commit 90f1ca9 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 02:50:52 2024 +0800 Remove redundant definition commit fa2da1a Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 02:50:36 2024 +0800 projection functions commit 54038ae Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 02:31:37 2024 +0800 join inclusions are null commit 313b74e Author: Trebor-Huang <treborhuang@foxmail.com> Date: Mon Aug 12 00:22:40 2024 +0800 Use pushout squares for cofibInl-⋁ commit d0a06cd Author: Trebor-Huang <treborhuang@foxmail.com> Date: Sun Aug 11 21:40:16 2024 +0800 pushout along identity commit b4e74c1 Author: Trebor-Huang <treborhuang@foxmail.com> Date: Sun Aug 11 21:08:23 2024 +0800 Susp is Pushout 1 <- X -> 1 commit 5dae632 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Sep 17 01:01:18 2024 +0200 fixes commit e13f9ab Merge: 10aea90 e2370fb Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Sep 16 22:22:28 2024 +0200 Merge remote-tracking branch 'master/master' into cellular_pointed commit 10aea90 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 14:42:34 2024 +0200 minor commit 1dff2d5 Merge: 46482af a0b4ba3 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 14:39:52 2024 +0200 merge commit 46482af Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 14:22:49 2024 +0200 connected clean commit 787f34f Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 14:12:57 2024 +0200 connected done? commit 73afa8e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 02:59:48 2024 +0200 cleaning commit 0cb5678 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jun 4 02:59:42 2024 +0200 cleaning commit 6bc3664 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Fri May 31 18:51:51 2024 +0200 pretty much done commit e4f4003 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Fri May 31 04:09:48 2024 +0200 almost commit c7acbee Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed May 29 18:11:46 2024 +0200 stuff commit 77623bb Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon May 27 03:16:45 2024 +0200 wip... commit dac2fd3 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu May 23 18:08:06 2024 +0200 stuff commit afe51a4 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed May 8 18:20:52 2024 +0200 p2 commit 87fa4c0 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue May 7 18:15:55 2024 +0200 done? commit eb6b12e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue May 7 10:12:34 2024 +0200 Pointed commit 3784dcd Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu May 2 11:34:11 2024 +0200 comments commit beccacd Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 12:03:53 2024 +0100 ojdå commit 3e53282 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 11:31:38 2024 +0100 broken code commit ac5249e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 09:39:57 2024 +0100 wups commit 1b005a6 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 02:22:00 2024 +0100 ugh commit 2d3fe1c Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 01:48:45 2024 +0100 wups commit b1f9e1d Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 01:30:09 2024 +0100 readme commit 6e259af Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Mar 4 00:38:02 2024 +0100 cleanup commit a3f6a9e Merge: 6ce70a4 f4745a2 4ba3c8e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Sun Mar 3 21:13:21 2024 +0100 merge commit 4ba3c8e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Sun Mar 3 20:55:52 2024 +0100 stuff commit a3bb47e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Sun Mar 3 20:48:17 2024 +0100 done? commit 53bb0f2 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Sun Mar 3 03:52:29 2024 +0100 stuff commit 54c7919 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Fri Mar 1 19:08:20 2024 +0100 stuff commit 42d6b77 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Feb 29 15:34:05 2024 +0100 stuff commit df55d55 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Feb 29 02:49:34 2024 +0100 More commit ae6e813 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Feb 27 00:10:56 2024 +0100 stuf commit b694120 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Feb 26 16:42:26 2024 +0100 stuff commit ea5fefd Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Sun Feb 25 23:02:26 2024 +0100 stuff commit f4745a2 Merge: 1c0396c 227b10b Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed Jan 31 10:49:17 2024 +0100 Merge remote-tracking branch 'origin/master' commit 9071481 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed Jan 31 10:46:56 2024 +0100 stuff commit e47bad5 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed Jan 24 19:53:25 2024 +0100 wups commit f7524eb Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 19:44:57 2024 +0100 ugh... commit b7716a4 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 19:19:56 2024 +0100 fixes commit 7313a31 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 15:04:18 2024 +0100 wups commit 7875e3e Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 14:51:05 2024 +0100 wups commit 74a8521 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 14:47:14 2024 +0100 wups commit 5e8b305 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 14:17:35 2024 +0100 done? commit 74596b5 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Jan 23 03:52:06 2024 +0100 .. commit 2b8b5fd Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Jan 22 18:50:46 2024 +0100 more commit 2fef4ef Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Jan 22 18:36:10 2024 +0100 stuff commit c034578 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Jan 18 17:17:24 2024 +0100 stuff commit 9d1915d Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Wed Jan 17 02:53:26 2024 +0100 fix commit 227b10b Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Jun 8 09:45:56 2023 +0200 w commit 3acc6b8 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Jun 8 09:45:28 2023 +0200 w commit ea75092 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Jun 8 09:44:37 2023 +0200 w commit 52429ff Merge: 9341710 814d54b Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Thu Jun 8 09:38:02 2023 +0200 Merge branch 'newM' commit 9341710 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Fri Jun 2 15:04:54 2023 +0200 ganea stuff commit 17f3fc1 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Apr 24 17:13:52 2023 +0200 rme commit aadde33 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Apr 24 17:12:41 2023 +0200 wups commit e8244ac Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Apr 24 17:10:45 2023 +0200 duplicate commit cc6ced2 Merge: b4b6efb f0ad815 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Mon Apr 24 17:10:10 2023 +0200 done commit b4b6efb Merge: 93d7248 9acdecf Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Feb 1 04:02:50 2022 +0100 m commit 93d7248 Author: aljungstrom <axel.ljungstrom@hotmail.com> Date: Tue Feb 1 04:00:15 2022 +0100 t
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Facilities for equational reasoning involving mixed use of
<
,≤
,≡
in a type that is both a quoset and a poset (with the additional data of<-≤-trans
,≤-<-trans
) to obtain a strict inequality (having at least a<
in the chain).This is inspired from
Relation.Binary.Reasoning.PartialOrder
of the Agda Standard Library.Some notes:
Such a chain can be written without nested equations, but it is not recomended, since it will perform a bunch of
subst
s, and the combinators from Prelude (such as_ ≡[ i ]⟨ p i ⟩ _
) cannot be used.begin
is needed at the start of the chain, since it has to extract a strict inequality from the given chain.<
won't be required in the chain.