Theorems · Definition · group theory
FreeGroup.freeGroupCongr
{α : Type u_1} → {β : Type u_2} → α ≃ β → FreeGroup α ≃* FreeGroup βEquivalent types give rise to multiplicatively equivalent free groups.
The converse can be found in Mathlib/GroupTheory/FreeGroup/GeneratorEquiv.lean, as
Equiv.ofFreeGroupEquiv.
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement and proof · cited by 8,337
- Equiv.symmproof · cited by 3,681
- MulEquivstatement · cited by 1,142
- FreeGroupstatement and proof · cited by 132
- FreeGroup.mapproof · cited by 20
Cited by11
Results whose statement or proof uses this declaration.
- CoxeterMatrix.reindexGroupEquivproof · cited by 3
- FreeGroupBasis.reindexproof · cited by 2
- PresentedGroup.equivPresentedGroupstatement and proof · cited by 2
- FreeGroup.freeGroupCongr_applystatement and proof · cited by 1
- FreeGroup.freeGroupCongr_reflstatement · cited by 0
- FreeGroup.freeGroupCongr_symmstatement · cited by 0
- FreeGroup.freeGroupCongr_transstatement · cited by 0
- CoxeterMatrix.reindex_relationsSetstatement and proof · cited by 0
- Group.fg_iff_exists_freeGroup_hom_surjective_finiteproof · cited by 0
- PresentedGroup.equivPresentedGroup_apply_ofstatement · cited by 0
- PresentedGroup.equivPresentedGroup_symm_apply_ofstatement · cited by 0