Theorems · Theorem · group theory
PresentedGroup.one_of_mem
∀ {α : Type u_1} {rels : Set (FreeGroup α)} {x : FreeGroup α}, x ∈ rels → (PresentedGroup.mk rels) x = 1- Defined in
- Mathlib.GroupTheory.PresentedGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MonoidHomstatement · cited by 3,629
- FreeGroupstatement and proof · cited by 132
- PresentedGroupstatement · cited by 21
- PresentedGroup.mkstatement · cited by 10
- Subgroup.subset_normalClosureproof · cited by 9
- PresentedGroup.mk_eq_one_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- PresentedGroup.lift_toCoprod_eq_oneproof · cited by 0
- PresentedGroup.mk_eq_mk_of_inv_mul_memproof · cited by 0
- PresentedGroup.mk_eq_mk_of_mul_inv_memproof · cited by 0