Theorems · Theorem · commutative algebra
Subsemiring.closure_submonoid_closure
∀ {R : Type u} [inst : NonAssocSemiring R] (s : Set R),
Subsemiring.closure ↑(Submonoid.closure s) = Subsemiring.closure s- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites14
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
- Submonoidstatement · cited by 3,086
- le_antisymmproof · cited by 2,068
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- Submonoid.closurestatement and proof · cited by 167
- Subsemiring.toSubmonoidproof · cited by 153
- Subsemiring.closurestatement and proof · cited by 53
- Submonoid.subset_closureproof · cited by 46
- Subsemiring.subset_closureproof · cited by 13
- Subsemiring.closure_leproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Subsemiring.coe_closure_eqproof · cited by 1