Theorems · Theorem · ring theory
Algebra.adjoin_nat
∀ {R : Type u_1} [inst : Semiring R] (s : Set R), Algebra.adjoin ℕ s = subalgebraOfSubsemiring (Subsemiring.closure s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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
- Semiringstatement and proof · cited by 13,802
- le_antisymmproof · cited by 2,068
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Algebra.subset_adjoinproof · cited by 109
- Subsemiring.closurestatement · cited by 53
- Algebra.adjoin_leproof · cited by 36
- Subsemiring.subset_closureproof · cited by 13
- Subsemiring.closure_leproof · cited by 12
- subalgebraOfSubsemiringstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.unitization_rangeproof · cited by 0