Mathlib Map

Theorems · Inductive type · ring theory

StarSubsemiring

(R : Type v) → [NonAssocSemiring R] → [Star R] → Type v

A (unital) star subsemiring is a non-associative ring which is closed under the star operation.

Defined in
Mathlib.Algebra.Star.Subsemiring
Cited by
18 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
NonAssocSemiringStar
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Around this declaration

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

StarSubsemiring.toSubsemiring · cited by 7StarSubsemiring.toSubsemi…StarSubsemiring.center · cited by 2StarSubsemiring.centerCentroidHom.starCenterIsoCentroid · cited by 2CentroidHom.starCenterIso…StarSubsemiring.copy · cited by 2StarSubsemiring.copyStarSubsemiring.ext · cited by 2StarSubsemiring.extStarSubsemiring.mk.inj · cited by 1mk.injStarSubsemiring.mk.noConfusion · cited by 1mk.noConfusionStarSubsemiring.mem_toSubsemiring · cited by 1StarSubsemiring.mem_toSub…StarSubsemiring.ofClass · cited by 1StarSubsemiring.ofClassStarSubsemiring.toSubsemiring_injective · cited by 1StarSubsemiring.toSubsemi…StarSubsemiring.toSubsemiring_le_iff · cited by 0StarSubsemiring.toSubsemi…StarSubsemiring.mk.injEq · cited by 0mk.injEqStarSubsemiring.mk.sizeOf_spec · cited by 0mk.sizeOf_specStarSubsemiring.casesOn · cited by 0StarSubsemiring.casesOnCentroidHom.starCenterIsoCentroid_apply · cited by 0CentroidHom.starCenterIso…NonAssocSemiring · cited by 805NonAssocSemiringStar · cited by 496StarStarSubsemiringCITED BYCITES

Cites2

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

Cited by29

Results whose statement or proof uses this declaration.