Theorems · Theorem · group theory
Monoid.exponent_eq_zero_iff
∀ {G : Type u} [inst : Monoid G], Monoid.exponent G = 0 ↔ ¬Monoid.ExponentExists G- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Monoid.exponentstatement · cited by 128
- Iff.not_rightproof · cited by 20
- Monoid.ExponentExistsstatement · cited by 18
- Monoid.exponent_ne_zeroproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Monoid.exponent_eq_zero_of_order_zeroproof · cited by 4
- Monoid.exponent_eq_iSup_orderOfproof · cited by 2
- Monoid.exponent_pi_eq_zeroproof · cited by 0
- Monoid.exponent_eq_sInfproof · cited by 0
- Monoid.exponent_eq_zero_iff_forallproof · cited by 0