Theorems · Definition · commutative algebra
Subsemiring.closure
{R : Type u} → [inst : NonAssocSemiring R] → Set R → Subsemiring RThe Subsemiring generated by a set.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- InfSet.sInfproof · cited by 935
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
Cited by58
Results whose statement or proof uses this declaration.
- Algebra.adjoinproof · cited by 535
- Subsemiring.subset_closurestatement · cited by 13
- Subsemiring.closure_lestatement · cited by 12
- Algebra.gcproof · cited by 7
- Subsemiring.gistatement and proof · cited by 6
- Subsemiring.closure_monostatement · cited by 4
- Algebra.adjoin_toSubsemiringstatement · cited by 4
- Subsemiring.closure_eqstatement · cited by 3
- Subsemiring.closure_inductionstatement and proof · cited by 3
- Subsemiring.closure_singleton_natCaststatement · cited by 3
- Algebra.adjoin_eq_ring_closureproof · cited by 2