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Theorems · Definition · order theory

Submonoid.oneLE

(M : Type u_1) → [inst : Monoid M] → [inst_1 : Preorder M] → [MulLeftMono M] → Submonoid M

The submonoid of elements that are at least 1.

Defined in
Mathlib.Algebra.Order.Monoid.Submonoid
Cited by
4 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
MonoidPreorderMulLeftMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

GroupCone.oneLE · cited by 4GroupCone.oneLESubmonoid.oneLE.congr_simp · cited by 0oneLE.congr_simpGroupCone.oneLE_toSubmonoid · cited by 0GroupCone.oneLE_toSubmono…Submonoid.mem_oneLE · cited by 0Submonoid.mem_oneLESubmonoid.coe_oneLE · cited by 0Submonoid.coe_oneLEPreorder · cited by 7952PreorderMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidSet.Ici · cited by 1070Set.IciMulLeftMono · cited by 410MulLeftMonoSubmonoid.oneLECITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.