Mathlib Map

Theorems · Theorem · order theory

IsOrderedMonoid.mkOfCone

∀ {S : Type u_1} {G : Type u_2} [inst : CommGroup G] [inst_1 : SetLike S G] (C : S) [inst_2 : GroupConeClass S G],
  have x := PartialOrder.mkOfGroupCone C;
  IsOrderedMonoid G

Construct a partially ordered abelian group by designating a cone in an abelian group.

Defined in
Mathlib.Algebra.Order.Group.Cone
Cited by
0 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext
Assumes
CommGroupSetLikeGroupConeClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

PartialOrder · cited by 6410PartialOrderSetLike · cited by 1084SetLikeCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoidmul_div_mul_right_eq_div · cited by 4mul_div_mul_right_eq_divGroupConeClass · cited by 3GroupConeClassPartialOrder.mkOfGroupCone · cited by 2PartialOrder.mkOfGroupConeIsOrderedMonoid.mkOfConeCITED BYCITES

Cites7

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.