Theorems · Theorem · linear algebra
Submodule.subset_span_finite_of_subset_span
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Set M}
{t : Finset M}, ↑t ⊆ ↑(Submodule.span R s) → ∃ T, ↑T ⊆ s ∧ ↑t ⊆ ↑(Submodule.span R ↑T)- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- LE.le.transproof · cited by 3,151
- Submodule.spanstatement and proof · cited by 1,504
- le_sup_leftproof · cited by 265
- Finset.induction_onproof · cited by 167
- Finset.mem_insert_selfproof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.fg_span_iff_fg_span_finset_subsetproof · cited by 0