Theorems · Theorem · group theory
zmultiples_abs
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] (g : G),
AddSubgroup.zmultiples |g| = AddSubgroup.zmultiples g- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- AddSubgroupstatement · cited by 3,232
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- AddSubgroup.zmultiples_negproof · cited by 6
- abs_casesproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.strictPeriods_eq_zmultiples_strictWidthInftyproof · cited by 4