Theorems · Theorem · commutative algebra
Subsemiring.closure_eq
∀ {R : Type u} [inst : NonAssocSemiring R] (s : Subsemiring R), Subsemiring.closure ↑s = sClosure of a subsemiring S equals S.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 3 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subsemiring.closurestatement · cited by 53
- GaloisInsertion.l_u_eqproof · cited by 37
- Subsemiring.giproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.sSup_toSubsemiringproof · cited by 1
- Algebra.sup_toSubsemiringproof · cited by 0
- Subsemiring.closure_univproof · cited by 0