feat(GroupTheory/FinitelyPresentedGroup): add finitely presented groups #34236
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- Add equivalence lemmas (incomplete) - Add basic instances (incomplete) Working on: isFinitelyPresented_iff_finite_set forward direction
- Add equivalence lemmas (incomplete) - Add basic instances (incomplete) Working on: isFinitelyPresented_iff_finite_set forward direction
…NormalClosureOfFiniteSet f'.ker`. Draft until I can figure out cleaner ways to do it.
…s more descriptive for groups.
…er_comp_mulEquiv` lemma.
…f (wip) and recovered instance
…stead of `α : Type`.
…ntedGroup G` draft human pf
Co-authored-by: Laurance Lau <60111599+LLaurance@users.noreply.github.com>
… `freeGroupUnitMulEquivInt`
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…ith an isomorphism (#34580) feat(Algebra/Group/Subgroup/Ker): kernel of a homomorphism composed with an isomorphism The kernel of a homomorphism composed with an isomorphism is equal to the kernel of the homomorphism mapped by the inverse isomorphism. This is a dependency of a larger PR to formalize finitely presented groups #34236.
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…ith an isomorphism (leanprover-community#34580) feat(Algebra/Group/Subgroup/Ker): kernel of a homomorphism composed with an isomorphism The kernel of a homomorphism composed with an isomorphism is equal to the kernel of the homomorphism mapped by the inverse isomorphism. This is a dependency of a larger PR to formalize finitely presented groups leanprover-community#34236.
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Formulation of finitely presented groups
feat(GroupTheory/FinitelyPresentedGroup): add finitely presented groups
We define the notion of
IsPresentedandIsFinitelyPresentedwith equivalent datatype notions, what it means for a subgroup to be finitely generated in the normal closure, and some instances of finitely presented groups.This started as an ItaLean2025 project. The related Zulip thread is here: https://leanprover.zulipchat.com/#narrow/channel/541885-ItaLean-2025/topic/Projects.3A.20Finitely.20Presented.20Groups/with/567565752.
Use of AI: Aristotle was used for giving a preliminary proof of some statements as this is my first contribution and I wanted to understand how to prove things; they have since been changed. ChatGPT was used to generate some of the proof sub-statements for efficiency once the mathematical blueprints of the proofs have been worked out.