Theorems · Theorem · group theory
AddRightCancelMonoid.finite_multiples
∀ {G : Type u_1} [inst : AddRightCancelMonoid G] {a : G}, (↑(AddSubmonoid.multiples a)).Finite ↔ IsOfFinAddOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddRightCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- Set.Finitestatement and proof · cited by 1,814
- AddSubmonoidstatement · cited by 1,178
- SetLike.mem_coeproof · cited by 302
- tsub_add_cancel_of_leproof · cited by 112
- IsOfFinAddOrderstatement · cited by 105
- add_nsmulproof · cited by 44
- AddSubmonoid.multiplesstatement and proof · cited by 40
- tsub_pos_iff_ltproof · cited by 27
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- AddRightCancelMonoid.infinite_multiplesproof · cited by 1