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Theorems · Theorem · group theory

Monoid.exponent_ne_zero_of_finite

∀ {G : Type u} [inst : LeftCancelMonoid G] [Finite G], Monoid.exponent G ≠ 0
Defined in
Mathlib.GroupTheory.Exponent
Cited by
2 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LeftCancelMonoidFinite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsZGroup.exponent_eq_card · cited by 0IsZGroup.exponent_eq_cardMonoid.one_lt_exponent · cited by 0Monoid.one_lt_exponentFinite · cited by 3029FiniteMonoid.exponent · cited by 128Monoid.exponentLeftCancelMonoid · cited by 28LeftCancelMonoidMonoid.ExponentExists.exponent_ne_zero · cited by 2ExponentExists.exponent_n…Monoid.ExponentExists.of_finite · cited by 2ExponentExists.of_finiteMonoid.exponent_ne_zero_of_fi…CITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.