Mathlib Map

Theorems · Definition · order theory

PartialOrder.mkOfAddGroupCone

{S : Type u_1} →
  {G : Type u_2} → [inst : AddCommGroup G] → [inst_1 : SetLike S G] → S → [AddGroupConeClass S G] → PartialOrder G

Construct a partial order by designating a cone in an abelian group.

Defined in
Mathlib.Algebra.Order.Group.Cone
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext
Assumes
AddCommGroupSetLikeAddGroupConeClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsOrderedAddMonoid.mkOfCone · cited by 0IsOrderedAddMonoid.mkOfCo…LinearOrder.mkOfAddGroupCone · cited by 0LinearOrder.mkOfAddGroupC…IsOrderedRing.mkOfCone · cited by 0IsOrderedRing.mkOfConePartialOrder.mkOfAddGroupCone_le_iff · cited by 0PartialOrder.mkOfAddGroup…AddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderSetLike · cited by 1084SetLikeAddGroupConeClass · cited by 3AddGroupConeClassPartialOrder.mkOfAddGroupConeCITED BYCITES

Cites4

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.