Theorems · Theorem · commutative algebra
Subsemiring.closure_addSubmonoid_closure
∀ {R : Type u} [inst : NonAssocSemiring R] {s : Set R},
Subsemiring.closure ↑(AddSubmonoid.closure s) = Subsemiring.closure s- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 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.
Cites19
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.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- AddSubmonoidstatement · cited by 1,178
- Set.iInterproof · cited by 1,084
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- AddSubmonoid.closurestatement and proof · cited by 224
- Submonoid.closureproof · cited by 167
- Subsemiring.toSubmonoidproof · cited by 153
- AddSubmonoid.subset_closureproof · cited by 63
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.