Theorems · Theorem · commutative algebra
Subsemiring.closure_singleton_natCast
∀ {R : Type u} [inst : NonAssocSemiring R] (n : ℕ), Subsemiring.closure {↑n} = ⊥- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Bot.botstatement and proof · cited by 4,720
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- Set.singleton_subset_iffproof · cited by 206
- bot_uniqueproof · cited by 57
- Subsemiring.closurestatement · cited by 53
- Subsemiring.closure_leproof · cited by 12
- natCast_memproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Subsemiring.closure_insert_natCastproof · cited by 2
- Subsemiring.closure_singleton_oneproof · cited by 0
- Subsemiring.closure_singleton_zeroproof · cited by 0