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Theorems · Theorem · group theory

AddSubmonoid.mem_multiples_iff

∀ {M : Type u_1} [inst : AddMonoid M] (x z : M), x ∈ AddSubmonoid.multiples z ↔ ∃ n, n • z = x
Defined in
Mathlib.Algebra.Group.Submonoid.Membership
Cited by
2 results in Mathlib
Foundations
Depth 24 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.

AddRightCancelMonoid.finite_multiples · cited by 1AddRightCancelMonoid.fini…finite_multiples · cited by 1finite_multiplesAddMonoid · cited by 2864AddMonoidAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.multiples · cited by 40AddSubmonoid.multiplesAddSubmonoid.mem_multiples_iffCITED BYCITES

Cites3

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Cited by2

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