Mathlib Map

Theorems · Definition · group theory

Submonoid.pos

(α : Type u_1) →
  [inst : MulZeroOneClass α] →
    [inst_1 : PartialOrder α] → [PosMulStrictMono α] → [ZeroLEOneClass α] → [NeZero 1] → Submonoid α

The submonoid of positive elements.

Defined in
Mathlib.Algebra.Order.GroupWithZero.Submonoid
Cited by
3 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
MulZeroOneClassPartialOrderPosMulStrictMonoZeroLEOneClassNeZero
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Around this declaration

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

Units.posSubgroup · cited by 4Units.posSubgroupSubmonoid.coe_pos · cited by 0Submonoid.coe_posSubmonoid.pos.congr_simp · cited by 0pos.congr_simpSubmonoid.mem_pos · cited by 0Submonoid.mem_posPartialOrder · cited by 6410PartialOrderSubmonoid · cited by 3086SubmonoidSet.Ioi · cited by 1463Set.IoiZeroLEOneClass · cited by 304ZeroLEOneClassMulZeroOneClass · cited by 184MulZeroOneClassPosMulStrictMono · cited by 151PosMulStrictMonoSubmonoid.posCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.