Theorems · Definition · ring theory
NonUnitalSubsemiring.closure
{R : Type u} → [inst : NonUnitalNonAssocSemiring R] → Set R → NonUnitalSubsemiring RThe NonUnitalSubsemiring generated by a set.
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- InfSet.sInfproof · cited by 935
- NonUnitalSubsemiringstatement and proof · cited by 201
Cited by34
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.adjoinproof · cited by 33
- NonUnitalSubsemiring.subset_closurestatement · cited by 10
- NonUnitalSubsemiring.closure_lestatement · cited by 8
- NonUnitalSubsemiring.gistatement and proof · cited by 6
- NonUnitalAlgebra.gcproof · cited by 5
- NonUnitalSubsemiring.mem_closurestatement · cited by 2
- Subsemigroup.nonUnitalSubsemiringClosure_eq_closurestatement and proof · cited by 2
- NonUnitalSubsemiring.closure_monostatement · cited by 2
- NonUnitalSubsemiring.mem_closure_iffstatement · cited by 1
- NonUnitalSubsemiring.mem_closure_of_memstatement · cited by 1
- NonUnitalAlgebra.mem_botproof · cited by 1
- NonUnitalSubsemiring.closure_emptystatement · cited by 1