Theorems · Theorem · linear algebra
finrank_span_finset_le_card
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
(s : Finset M), Set.finrank R ↑s ≤ s.card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- 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
- Finset.cardstatement and proof · cited by 2,327
- StrongRankConditionstatement and proof · cited by 286
- Finset.toFinset_coeproof · cited by 16
- Set.finrankstatement · cited by 9
- finrank_span_le_cardproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- finrank_vectorSpan_image_finset_leproof · cited by 1