Theorems · Theorem · group theory
Monoid.exponent_eq_zero_iff_range_orderOf_infinite
∀ {G : Type u} [inst : Monoid G], (∀ (g : G), 0 < orderOf g) → (Monoid.exponent G = 0 ↔ (Set.range orderOf).Infinite)- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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.
- Set.rangestatement and proof · cited by 4,705
- Monoidstatement and proof · cited by 3,887
- Set.Finiteproof · cited by 1,814
- orderOfstatement and proof · cited by 324
- Set.Infinitestatement · cited by 263
- Monoid.exponentstatement and proof · cited by 128
- not_iff_commproof · cited by 32
- Monoid.exponent_ne_zero_iff_range_orderOf_finiteproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.exponent_eq_iSup_orderOfproof · cited by 2