Theorems · Theorem · commutative algebra
Subsemiring.closure_insert_natCast
∀ {R : Type u} [inst : NonAssocSemiring R] (n : ℕ) (s : Set R),
Subsemiring.closure (insert (↑n) s) = Subsemiring.closure s- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites8
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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- sup_of_le_rightproof · cited by 143
- Subsemiring.closurestatement and proof · cited by 53
- Set.insert_eqproof · cited by 47
- Subsemiring.closure_singleton_natCastproof · cited by 3
- Subsemiring.closure_unionproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subsemiring.closure_insert_zeroproof · cited by 1
- Subsemiring.closure_insert_oneproof · cited by 0