Theorems · Theorem · commutative algebra
Submodule.set_smul_top_eq_span
∀ {R : Type u_1} [inst : CommSemiring R] (s : Set R), s • ⊤ = Ideal.span s- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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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
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- Ideal.mul_topproof · cited by 42
- Submodule.pointwiseSetSMulstatement · cited by 30
- Submodule.span_smul_eqproof · cited by 6
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