Theorems · Theorem · ring theory
MonoidAlgebra.single_mem_span_single
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [Nontrivial R] {m : M} {s : Set M},
MonoidAlgebra.single m 1 ∈ Submodule.span R ((fun x => MonoidAlgebra.single x 1) '' s) ↔ m ∈ s- Defined in
- Mathlib.Algebra.MonoidAlgebra.Module
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Submodulestatement · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Nontrivialstatement and proof · cited by 2,416
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.toLinearMapproof · cited by 1,171
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement and proof · cited by 590
- Set.image_congrproof · cited by 533
- MonoidAlgebra.singlestatement and proof · cited by 253
- MonoidAlgebra.coeffproof · cited by 224
Cited by1
Results whose statement or proof uses this declaration.
- MonoidAlgebra.of_mem_span_of_iffproof · cited by 1