Theorems · Theorem · commutative algebra
natCast_mem
∀ {S : Type u_1} {R : Type u_2} [inst : AddMonoidWithOne R] [inst_1 : SetLike S R] (s : S)
[AddSubmonoidWithOneClass S R] (n : ℕ), ↑n ∈ s- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
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.
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- SetLikestatement and proof · cited by 1,084
- Nat.cast_addproof · cited by 586
- AddMonoidWithOnestatement and proof · cited by 313
- AddSubmonoidWithOneClassstatement and proof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Subsemiring.closure_singleton_natCastproof · cited by 3
- SubfieldClass.nnratCast_memproof · cited by 2
- SubfieldClass.ratCast_memproof · cited by 2
- Subalgebra.natCast_memproof · cited by 1
- natCast_memℓp_inftyproof · cited by 0
- ofNat_memproof · cited by 0