Theorems · Theorem · ring theory
NonUnitalSubsemiring.mem_closure_iff
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {s : Set R} {x : R},
x ∈ NonUnitalSubsemiring.closure s ↔ x ∈ AddSubmonoid.closure ↑(Subsemigroup.closure s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites11
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 · cited by 8,199
- AddSubmonoidstatement · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Subsemigroupstatement · cited by 323
- AddSubmonoid.closurestatement · cited by 224
- NonUnitalSubsemiringstatement · cited by 201
- Set.ext_iffproof · cited by 90
- Subsemigroup.closurestatement · cited by 43
- NonUnitalSubsemiring.closurestatement · cited by 31
- NonUnitalSubsemiring.coe_closure_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.closure_addSubmonoid_closureproof · cited by 0