To compile use make. This project has been tested using the following dependencies (packages) installed via opam:

Dependencies

Name	Installed	Synopsis
rocq	9.0.0	The Rocq Prover with Stdlib
coq-stdpp	1.11.0	An extended "Standard Library" for Coq
ocaml	5.3.0	The OCaml compiler (virtual package)

Project layout

.
+-- Readme.md
+-- Makefile
+-- _CoqProject
+-- theories/prelude.v (global parameters)
+-- theories/quotient.v (quotients in Rocq)
+-- theories/stepindex.v (ordinals interface)
+-- theories/ordinals (ordinals framework)
+-- theories/existential_prop
|   +-- classical.v (Choice+FunExt+PI->EM)
|   +-- sigma.v (equality of sigma-types)
|   +-- existential_prop.v (existential property)
+-- theories/categories/
|   +-- category.v (general constructions)
|   +-- contractive.v (subclass of locally contractive functors, example)
|   +-- coprod.v (coproducts)
|   +-- domain.v (uniqueness of solution, later is locally contractive, symmetrization, )
|   +-- enriched.v (partial isomorphisms and pointwise-enriched limits)
|   +-- logic.v (logical connectives for step-indexed logic)
|   +-- ord_cat.v (presheaves over ordinals, later, next, earlier, fixpoint)
|   +-- solution.v (solver for recursive domain equations)

Paper-formalization glossary

Paper entry	Rocq qualified identifier
later	SynthDom.categories.ord_cat.later
earlier	SynthDom.categories.ord_cat.earlier
next	SynthDom.categories.ord_cat.next
def. 3	SynthDom.categories.ord_cat.Contractive
lemma 4	SynthDom.categories.ord_cat.{Contractive_comp_l,Contractive_comp_r}
def. 5	SynthDom.categories.ord_cat.{fixpoint, fixpoint_unfold, fixpoint_unique}
theorem 7	SynthDom.categories.ord_cat.{contr_fix, contr_fix_unfold, contr_fix_unique}
def. 9	SynthDom.categories.category.Enriched
def. 10	SynthDom.categories.category.EnrichedFunctor
def. 11	SynthDom.categories.enriched.LocallyContractiveFunctor
lemma 12	SynthDom.categories.enriched.{LocallyContractiveFunctor_comp_l, LocallyContractiveFunctor_comp_r}
def. 13	SynthDom.categories.enriched.is_iso_at
lemma 15	SynthDom.categories.enriched.is_iso_upto_total
lemma 16	SynthDom.categories.enriched.is_iso_at_func
lemma 17	SynthDom.categories.enriched.iso_upto_contr_func
def. 18	SynthDom.categories.enriched.enr_cone
def. 19	SynthDom.categories.enriched.enr_cone_hom
def. 20	SynthDom.categories.enriched.enr_cone_is_limit
lemma 21	SynthDom.categories.enriched.{strongly_connected_iso_at_diagram_enr_cone, limit_side_iso_at', limit_side_iso_at}
corollary 22	SynthDom.categories.enriched.limit_side_iso_at_cofinal
theorem 23	SynthDom.categories.domain.alg_of_solution_is_initial
def. 24	SynthDom.categories.solution.partial_solution
def. 25	SynthDom.categories.solution.par_sol_extension
lemma 26	SynthDom.categories.solution.the_extension
def. 27	SynthDom.categories.solution.is_canonical_par_sol
lemma 28	SynthDom.categories.solution.canonical_eq
lemma 29	SynthDom.categories.solution.tower
theorem 30	SynthDom.categories.solution.solver
example 32	SynthDom.categories.solution.simplified_gitree_dom
lemma 33	SynthDom.categories.domain.symmetrization_sol
theorem 34	SynthDom.existential_prop.existential_prop.forall_exists_swap
def. 36	SynthDom.existential_prop.existential_prop.regular
theorem 37	SynthDom.categories.domain.{later_enriched, later_lc}
remark 40	SynthDom.categories.enriched.{isomorphism_at_id, compose_along_isomorphism_at_left, compose_along_isomorphism_at_right, compose_along_is_iso_at_left, compose_along_is_iso_at_right, compose_along_is_iso_at_left', compose_along_is_iso_at_right', is_iso_at_compose, is_iso_at_uncompose_l, is_iso_at_uncompose_r}
theorem 42	SynthDom.categories.ord_cat.later_adj
theorem 43	SynthDom.categories.category.{func_limit, func_cat_limits_pointwise}
theorem 44	SynthDom.categories.category.alg_complete

Notation glossary

Category theory

Construction	Rocq notation
Isomorphism	≃
Terminal object	1ₒ
Products	a ×ₒ b
Unique product morphism	<< f, g >>
Product of morphisms	f ×ₕ g
Coproduct	a +ₒ b
Unique coproduct morphism	<< f ∣ g >>
Coproduct of morphisms	f +ₕ g
Exponential	b ↑ₒ a
Functor object action	F ₒ a
Functor morphism action	F ₕ f
Natural transformation component	H ₙ a