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Theorems · Definition · ring theory

NonUnitalSubsemiring.toAddSubmonoid

{R : Type u} → [inst : NonUnitalNonAssocSemiring R] → NonUnitalSubsemiring R → AddSubmonoid R

Reinterpret a NonUnitalSubsemiring as an AddSubmonoid.

Defined in
Mathlib.RingTheory.NonUnitalSubsemiring.Defs
Cited by
56 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
NonUnitalNonAssocSemiring
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Around this declaration

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

NonUnitalStarAlgebra.adjoin · cited by 43NonUnitalStarAlgebra.adjo…NonUnitalSubalgebra.map · cited by 23NonUnitalSubalgebra.mapNonUnitalSubalgebra.toSubmodule · cited by 23NonUnitalSubalgebra.toSub…NonUnitalSubsemiring.map · cited by 22NonUnitalSubsemiring.mapNonUnitalSubring.map · cited by 19NonUnitalSubring.mapSubsemiring.center · cited by 18Subsemiring.centerNonUnitalSubring.comap · cited by 15NonUnitalSubring.comapNonUnitalSubsemiring.comap · cited by 14NonUnitalSubsemiring.comapNonUnitalSubsemiring.toSubsemigroup · cited by 12NonUnitalSubsemiring.toSu…NonUnitalSubring.toAddSubgroup · cited by 10NonUnitalSubring.toAddSub…NonUnitalSubsemiring.prod · cited by 9NonUnitalSubsemiring.prodNonUnitalSubalgebra.starClosure · cited by 8NonUnitalSubalgebra.starC…NonUnitalSubring.toSubsemigroup · cited by 8NonUnitalSubring.toSubsem…NonUnitalSubsemiring.topologicalClosure · cited by 5NonUnitalSubsemiring.topo…Subsemiring.sumSq · cited by 4Subsemiring.sumSqAddSubmonoid · cited by 1178AddSubmonoidNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringNonUnitalSubsemiring.toAddSub…CITED BYCITES

Cites3

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

Cited by97

Results whose statement or proof uses this declaration.