Theorems · Theorem · commutative algebra
Ideal.subset_span
∀ {α : Type u} [inst : Semiring α] {s : Set α}, s ⊆ ↑(Ideal.span s)- Defined in
- Mathlib.RingTheory.Ideal.Span
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- Semiring
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.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement · cited by 8,199
- Idealstatement · cited by 4,748
- Ideal.spanstatement · cited by 948
- Submodule.subset_spanproof · cited by 234
Cited by86
Results whose statement or proof uses this declaration.
- Ideal.mem_map_of_memproof · cited by 71
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Ideal.map_spanproof · cited by 43
- Ideal.span_singleton_oneproof · cited by 21
- Ideal.map_topproof · cited by 17
- Algebra.Presentation.relation_mem_kerproof · cited by 9
- Nat.setGcd_dvd_of_memproof · cited by 5
- Algebra.Presentation.aeval_val_relationproof · cited by 5
- Ideal.IsMaximal.exists_invproof · cited by 4
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- Ideal.span_pow_eq_topproof · cited by 4
- Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_selfproof · cited by 3