├── .github └── workflows │ ├── docker-action.yml │ └── nix-action-default.yml ├── .gitignore ├── .gitpod.yml ├── .nix ├── config.nix ├── coq-nix-toolbox.nix ├── coq-overlays │ ├── goedel │ │ └── default.nix │ ├── hydra-battles-single │ │ └── default.nix │ └── hydra-battles │ │ └── default.nix ├── gitpod.Dockerfile └── nixpkgs.nix ├── LICENSE ├── Makefile ├── Makefile.coq.local ├── README.md ├── _CoqProject ├── coq-addition-chains.opam ├── coq-gaia-hydras.opam ├── coq-goedel.opam ├── coq-hydra-battles.opam ├── default.nix ├── doc ├── .gitignore ├── Gamma0-chapter.tex ├── JFLA2022 │ ├── E0_Ex42.tex │ ├── Hprime_HprimeDef.tex │ ├── Makefile │ ├── Pow_evalPow17LetIn.tex │ ├── README.md │ ├── Schutte_Ex42a.tex │ ├── Schutte_Ex42b.tex │ ├── Schutte_Ex42c.tex │ ├── Schutte_Ex42d.tex │ ├── Schutte_Ex42e.tex │ ├── SimpleMakefile │ ├── Slides │ │ ├── HprimePhi0OmegaClosed.tex │ │ ├── Makefile │ │ ├── ONDef.tex │ │ ├── SchemePrimRecInda.tex │ │ ├── Slides.tex │ │ ├── alectryon.sty │ │ ├── canonDef.tex │ │ ├── gcanonLimitOf.tex │ │ ├── gcanonSLE.tex │ │ ├── macros.tex │ │ ├── multA.tex │ │ └── tsukubabooks.jpg │ ├── alectryon.sty │ ├── easychair.cls │ ├── easychair.tex │ ├── paper.bbl │ ├── paper.tex │ ├── pygments.sty │ └── snippets │ │ ├── E0 │ │ └── Ex42.tex │ │ ├── Hprime │ │ ├── HprimeDef.tex │ │ └── HprimeDefb.tex │ │ ├── Pow │ │ └── evalPow17LetIn.tex │ │ └── Schutte │ │ ├── Ex42a.tex │ │ ├── Ex42b.tex │ │ ├── Ex42c.tex │ │ ├── Ex42d.tex │ │ └── Ex42e.tex ├── Makefile ├── blue-hydra.jpg ├── chap-intro-goedel.tex ├── chapter-encoding.tex ├── chapter-expressible.tex ├── chapter-fol.tex ├── chapter-lnn-lnt.tex ├── chapter-natural-deduction.tex ├── chapter-powers.tex ├── chapter-primrec.tex ├── coqmacros.tex ├── epsilon0-chapter.tex ├── epsilon0.jpg ├── gaia-chapter.tex ├── hydra-chapter.tex ├── hydras.tex ├── hydre-pierrette.jpg ├── ks-chapter.tex ├── large-sets-chapter.tex ├── marginote.sty ├── movies │ ├── Makefile │ ├── Readme.md │ ├── config.mk │ ├── driver.py │ ├── extract_snippets.py │ ├── extract_snippets │ │ ├── Extractor.py │ │ ├── Reader.py │ │ ├── Snippet.py │ │ ├── __init__.py │ │ ├── cli.py │ │ ├── docutils.py │ │ └── snippetExceptions.py │ ├── gen_targets.py │ └── requirements.txt ├── multind.sty ├── ordinal-chapter.tex ├── part-hydras-intro.tex ├── proof.sty ├── rooster-hydra.png ├── schutte-chapter.tex ├── thebib.bib ├── turnstile.sty ├── tuto-beamer.tex └── tuto.tex ├── dune-project ├── exercises ├── README.md ├── ordinals │ ├── F_3.v │ ├── Limit_Infinity.v │ ├── T1_ltNotWf.v │ ├── ge_omega_iff.v │ ├── is_F_monotonous.v │ ├── lt_succ_le.v │ ├── predSuccUnicity.v │ └── schutte_cnf_counter_example.v └── primrec │ ├── FibonacciPR.v │ ├── MinPR.v │ ├── MorePRExamples.v │ └── isqrt.v ├── meta.yml ├── theories ├── additions │ ├── AM.v │ ├── Addition_Chains.v │ ├── BinaryStrat.v │ ├── Compatibility.v │ ├── Demo.v │ ├── Demo_power.v │ ├── Dichotomy.v │ ├── Euclidean_Chains.v │ ├── Fib2.v │ ├── FirstSteps.v │ ├── Monoid_def.v │ ├── Monoid_instances.v │ ├── More_on_positive.v │ ├── Naive.v │ ├── Pow.v │ ├── Pow_variant.v │ ├── Strategies.v │ ├── Trace_exercise.v │ ├── Wf_transparent.v │ ├── dune │ ├── fib.v │ ├── make_fib_tests.txt │ ├── solutions_exercises │ │ └── Computation_app.v │ └── stub.ml ├── gaia │ ├── GCanon.v │ ├── GF_alpha.v │ ├── GHessenberg.v │ ├── GHprime.v │ ├── GHydra.v │ ├── GL_alpha.v │ ├── GLarge_Sets.v │ ├── GPaths.v │ ├── GPrelude.v │ ├── GaiaToHydra.v │ ├── HydraGaia_Examples.v │ ├── ON_gfinite.v │ ├── T1Bridge.v │ ├── T1Choice.v │ ├── T2Bridge.v │ ├── dune │ ├── nfwfgaia.v │ └── onType.v ├── goedel │ ├── PRrepresentable.v │ ├── codeSysPrf.v │ ├── dune │ ├── fixPoint.v │ ├── goedel1.v │ ├── goedel2.v │ ├── rosser.v │ └── rosserPA.v └── ordinals │ ├── Ackermann │ ├── Deduction.v │ ├── LNN.v │ ├── LNN2LNT.v │ ├── LNT.v │ ├── Languages.v │ ├── ListExt.v │ ├── NN.v │ ├── NN2PA.v │ ├── NNtheory.v │ ├── NewNotations.v │ ├── PA.v │ ├── PAconsistent.v │ ├── PAtheory.v │ ├── cPair.v │ ├── checkPrf.v │ ├── code.v │ ├── codeFreeVar.v │ ├── codeList.v │ ├── codeNatToTerm.v │ ├── codePA.v │ ├── codeSubFormula.v │ ├── codeSubTerm.v │ ├── expressible.v │ ├── extEqualNat.v │ ├── fol.v │ ├── folLogic.v │ ├── folLogic2.v │ ├── folLogic3.v │ ├── folProof.v │ ├── folProp.v │ ├── folReplace.v │ ├── misc.v │ ├── model.v │ ├── prLogic.v │ ├── primRec.v │ ├── subAll.v │ ├── subProp.v │ ├── wConsistent.v │ └── wellFormed.v │ ├── Epsilon0 │ ├── Canon.v │ ├── E0.v │ ├── Epsilon0.v │ ├── Epsilon0rpo.v │ ├── F_alpha.v │ ├── F_omega.v │ ├── Hessenberg.v │ ├── Hprime.v │ ├── L_alpha.v │ ├── Large_Sets.v │ ├── Large_Sets_Examples.v │ ├── Paths.v │ └── T1.v │ ├── Gamma0 │ ├── Gamma0.v │ └── T2.v │ ├── Hydra │ ├── Battle_length.v │ ├── BigBattle.v │ ├── Epsilon0_Needed_Free.v │ ├── Epsilon0_Needed_Generic.v │ ├── Epsilon0_Needed_Std.v │ ├── Hydra_Definitions.v │ ├── Hydra_Examples.v │ ├── Hydra_Extraction.v │ ├── Hydra_Lemmas.v │ ├── Hydra_Termination.v │ ├── Hydra_Theorems.v │ ├── KP_example.v │ ├── O2H.v │ ├── Omega2_Small.v │ └── Omega_Small.v │ ├── MoreAck │ ├── Ack.v │ ├── AckNotPR.v │ ├── BadSubst.v │ ├── FolExamples.v │ ├── Iterate_compat.v │ ├── LNN_Examples.v │ ├── PrimRecExamples.v │ └── expressibleExamples.v │ ├── OrdinalNotations │ ├── Example_3PlusOmega.v │ ├── ON_Finite.v │ ├── ON_Generic.v │ ├── ON_O.v │ ├── ON_Omega.v │ ├── ON_Omega2.v │ ├── ON_Omega_plus_omega.v │ ├── ON_mult.v │ ├── ON_plus.v │ └── OmegaOmega.v │ ├── Prelude │ ├── Comparable.v │ ├── Compat815.v │ ├── DecPreOrder.v │ ├── DecPreOrder_Instances.v │ ├── Exp2.v │ ├── First_toggle.v │ ├── Fuel.v │ ├── Iterates.v │ ├── LibHyps_Experiments.v │ ├── Merge_Sort.v │ ├── MoreDecidable.v │ ├── MoreLibHyps.v │ ├── MoreLists.v │ ├── MoreOrders.v │ ├── MoreVectors.v │ ├── More_Arith.v │ ├── OrdNotations.v │ ├── Restriction.v │ ├── STDPP_compat.v │ ├── Simple_LexProd.v │ ├── Sort_spec.v │ ├── WfVariant.v │ └── ssrnat_extracts.v │ ├── Schutte │ ├── AP.v │ ├── Addition.v │ ├── CNF.v │ ├── Correctness_E0.v │ ├── Countable.v │ ├── Critical.v │ ├── GRelations.v │ ├── Lub.v │ ├── MoreEpsilonIota.v │ ├── Ordering_Functions.v │ ├── PartialFun.v │ ├── Schutte.v │ ├── Schutte_basics.v │ └── Well_Orders.v │ ├── dune │ ├── rpo │ ├── closure.v │ ├── decidable_set.v │ ├── dickson.v │ ├── list_permut.v │ ├── list_set.v │ ├── more_list.v │ ├── rpo.v │ └── term.v │ └── solutions_exercises │ ├── F_3.v │ ├── FibonacciPR.v │ ├── Limit_Infinity.v │ ├── MinPR.v │ ├── MinPR2.v │ ├── MorePRExamples.v │ ├── MultisetWf.v │ ├── OnCodeList.v │ ├── T1_ltNotWf.v │ ├── ge_omega_iff.v │ ├── is_F_monotonous.v │ ├── isqrt.v │ ├── lt_succ_le.v │ ├── omega_iterates.v │ ├── predSuccUnicity.v │ └── schutte_cnf_counter_example.v └── v09changes.md /.github/workflows/docker-action.yml: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rocq-community/hydra-battles/HEAD/.github/workflows/docker-action.yml 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