Theorems · Theorem · group theory
AddSubgroup.zmultiples_eq_zmultiples_iff
∀ {G : Type u_1} [inst : AddGroup G] {x y : G},
¬IsOfFinAddOrder x → (AddSubgroup.zmultiples x = AddSubgroup.zmultiples y ↔ x = y ∨ -x = y)- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- IsOfFinAddOrderstatement and proof · cited by 105
- one_nsmulproof · cited by 63
- one_zsmulproof · cited by 59
- neg_zsmulproof · cited by 41
- ofNat_zsmulproof · cited by 24
- mul_zsmul'proof · cited by 16
- AddSubgroup.mem_zmultiples_iffproof · cited by 11
- AddSubgroup.mem_zmultiplesproof · cited by 10
- AddSubgroup.zmultiples_negproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.strictWidthInfty_eq_one_of_T_memproof · cited by 3
- Int.addEquiv_eq_refl_or_negproof · cited by 0
- CongruenceSubgroup.strictWidthInfty_Gammaproof · cited by 0