Theorems · Definition · commutative algebra
Subsemiring.toAddSubmonoid
{R : Type u} → [inst : NonAssocSemiring R] → Subsemiring R → AddSubmonoid RReinterpret a Subsemiring as an AddSubmonoid.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubmonoidstatement · cited by 1,178
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
- Subsemiring.toSubmonoidproof · cited by 153
- Subsemiring.add_mem'proof · cited by 0
- Subsemiring.zero_mem'proof · cited by 0
Cited by29
Results whose statement or proof uses this declaration.
- Subsemiring.mapproof · cited by 29
- Subsemiring.comapproof · cited by 20
- Subsemiring.subtypeproof · cited by 11
- Subsemiring.prodproof · cited by 11
- Subsemiring.topologicalClosureproof · cited by 6
- Subsemiring.copyproof · cited by 5
- Subalgebra.toAddSubmonoidproof · cited by 2
- RingEquiv.subsemiringMapproof · cited by 2
- Subsemiring.mem_iSup_of_directedproof · cited by 2
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Subsemiring.toAddSubmonoid_strictMonostatement · cited by 1
- Subsemiring.matrixproof · cited by 1