Theorems · Theorem · linear algebra
Fintype.range_linearCombination
∀ {α : Type u_1} {M : Type u_2} (R : Type u_3) [inst : Fintype α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] (v : α → M), (Fintype.linearCombination R v).range = Submodule.span R (Set.range v)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Finsuppproof · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.isCompact_of_fgproof · cited by 2
- Submodule.FG.smallproof · cited by 1
- PiToModule.fromEnd_injectiveproof · cited by 1
- span_range_eq_top_iff_surjective_fintypeLinearCombinationproof · cited by 0