Theorems · Theorem · group theory
AddMonoid.exponent_eq_iSup_addOrderOf
∀ {G : Type u} [inst : AddCommMonoid G], (∀ (g : G), 0 < addOrderOf g) → AddMonoid.exponent G = ⨆ g, addOrderOf g- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Set.rangeproof · cited by 4,705
- iSupstatement · cited by 2,415
- SupSet.sSupproof · cited by 954
- addOrderOfstatement and proof · cited by 208
- Set.mem_rangeproof · cited by 102
- Set.range_nonemptyproof · cited by 84
- AddMonoid.exponentstatement and proof · cited by 70
- AddMonoid.ExponentExistsproof · cited by 17
- csSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
- exists_exists_eq_andproof · cited by 5
- AddMonoid.exponent_eq_zero_iffproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_eq_max'_addOrderOfproof · cited by 1
- AddMonoid.exponent_eq_iSup_addOrderOf'proof · cited by 0