Theorems · Theorem · linear algebra
finrank_span_set_eq_card
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
{s : Set M} [inst_4 : Fintype ↑s], LinearIndepOn R id s → Module.finrank R ↥(Submodule.span R s) = s.toFinset.card- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- Cardinalproof · cited by 2,598
- Finset.cardstatement · cited by 2,327
- Module.finrankstatement · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
- Cardinal.mkproof · cited by 942
Cited by4
Results whose statement or proof uses this declaration.
- ZLattice.rankproof · cited by 5
- Affine.Simplex.affineSpan_pair_eq_altitude_iffproof · cited by 2
- Pi.dim_spanSubsetproof · cited by 2
- finrank_span_finset_eq_cardproof · cited by 1