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Theorems · Theorem · group theory

AddMonoid.ExponentExists.exponent_ne_zero

∀ {G : Type u} [inst : AddMonoid G], AddMonoid.ExponentExists G → AddMonoid.exponent G ≠ 0

Alias of the reverse direction of AddMonoid.exponent_ne_zero.

Defined in
Mathlib.GroupTheory.Exponent
Cited by
2 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoid
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Around this declaration

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

AddMonoid.exponent_ne_zero_of_finite · cited by 1AddMonoid.exponent_ne_zer…AddMonoid.exists_addOrderOf_eq_exponent · cited by 1AddMonoid.exists_addOrder…AddMonoid · cited by 2864AddMonoidAddMonoid.exponent · cited by 70AddMonoid.exponentAddMonoid.ExponentExists · cited by 17AddMonoid.ExponentExistsAddMonoid.exponent_ne_zero · cited by 4AddMonoid.exponent_ne_zeroExponentExists.exponent_ne_ze…CITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.