Theorems · Theorem · group theory
Monoid.exponent_eq_iSup_orderOf
∀ {G : Type u} [inst : CommMonoid G], (∀ (g : G), 0 < orderOf g) → Monoid.exponent G = ⨆ g, orderOf 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
- CommMonoid
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.
- Set.rangeproof · cited by 4,705
- iSupstatement · cited by 2,415
- CommMonoidstatement and proof · cited by 2,264
- SupSet.sSupproof · cited by 954
- orderOfstatement and proof · cited by 324
- Monoid.exponentstatement and proof · cited by 128
- Set.range_nonemptyproof · cited by 84
- Monoid.ExponentExistsproof · cited by 18
- csSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
- Monoid.exponent_eq_zero_iffproof · cited by 5
- Set.Infinite.Nat.sSup_eq_zeroproof · cited by 3
- Monoid.orderOf_le_exponentproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Monoid.exponent_eq_max'_orderOfproof · cited by 1
- Monoid.exponent_eq_iSup_orderOf'proof · cited by 0