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Theorems · Theorem · group theory

isAddUnit_nsmul_iff

∀ {M : Type u_1} [inst : AddMonoid M] {n : ℕ} {a : M}, n ≠ 0 → (IsAddUnit (n • a) ↔ IsAddUnit a)
Defined in
Mathlib.Algebra.Group.Commute.Units
Cited by
2 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext
Assumes
AddMonoid
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Around this declaration

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

not_addIrreducible_nsmul · cited by 1not_addIrreducible_nsmulisAddUnit_nsmul_succ_iff · cited by 0isAddUnit_nsmul_succ_iffAddMonoid · cited by 2864AddMonoidAddUnits · cited by 325AddUnitsAddUnits.val · cited by 248AddUnits.valIsAddUnit · cited by 215IsAddUnitAddUnits.isAddUnit · cited by 14AddUnits.isAddUnitIsAddUnit.nsmul · cited by 4IsAddUnit.nsmulAddUnits.ofNSMul · cited by 1AddUnits.ofNSMulisAddUnit_nsmul_iffCITED BYCITES

Cites7

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.