Theorems · Theorem · linear algebra
span_flip_eq_top_iff_linearIndependent
∀ {ι : Type u_1} {α : Type u_2} {F : Type u_3} [Finite ι] [inst : Field F] {f : ι → α → F},
Submodule.span F (Set.range (flip f)) = ⊤ ↔ LinearIndependent F f- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Finsuppproof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Bot.botproof · cited by 4,720
- Set.rangestatement and proof · cited by 4,705
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.