Theorems · Theorem · group theory
not_isOfFinAddOrder_of_isAddTorsionFree
∀ {G : Type u_1} [inst : AddMonoid G] {a : G} [IsAddTorsionFree G], a ≠ 0 → ¬IsOfFinAddOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidIsAddTorsionFree
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.
- AddMonoidstatement and proof · cited by 2,864
- LT.lt.ne'proof · cited by 1,417
- IsAddTorsionFreestatement and proof · cited by 155
- IsOfFinAddOrderstatement · cited by 105
- nsmul_zeroproof · cited by 73
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- nsmul_right_injectiveproof · cited by 8
- nsmul_eq_zero_iffproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- isAddTorsionFree_iff_not_isOfFinAddOrderproof · cited by 4
- Subgroup.strictWidthInfty_eq_one_of_T_memproof · cited by 3
- LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_intproof · cited by 2
- AddMonoid.minOrder_eq_topproof · cited by 1
- IsOfFinAddOrder.eq_zero'proof · cited by 1
- CongruenceSubgroup.strictWidthInfty_Gammaproof · cited by 0
- Int.addEquiv_eq_refl_or_negproof · cited by 0