Theorems · Theorem · group theory
not_isOfFinOrder_of_isMulTorsionFree
∀ {G : Type u_1} [inst : Monoid G] {a : G} [IsMulTorsionFree G], a ≠ 1 → ¬IsOfFinOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsMulTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- LT.lt.ne'proof · cited by 1,417
- one_powproof · cited by 521
- IsOfFinOrderstatement · cited by 113
- IsMulTorsionFreestatement and proof · cited by 44
- isOfFinOrder_iff_pow_eq_oneproof · cited by 27
- pow_left_injectiveproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroup.Subgroup.genLTOne_uniqueproof · cited by 5
- isMulTorsionFree_iff_not_isOfFinOrderproof · cited by 2
- Monoid.minOrder_eq_topproof · cited by 1
- IsOfFinOrder.eq_one'proof · cited by 1