Theorems · Theorem · linear algebra
finrank_span_le_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], Module.finrank R ↥(Submodule.span R s) ≤ s.toFinset.card- Cited by
- 8 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Finset.cardstatement · cited by 2,327
- Module.finrankstatement · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
- Module.rankproof · cited by 496
- StrongRankConditionstatement and proof · cited by 286
Cited by8
Results whose statement or proof uses this declaration.
- finrank_span_singletonproof · cited by 16
- ZLattice.rankproof · cited by 5
- LinearEquiv.sup_span_singleton_lt_topproof · cited by 1
- finrank_le_of_span_eq_topproof · cited by 1
- finrank_range_le_cardproof · cited by 1
- finrank_span_finset_le_cardproof · cited by 1
- span_lt_of_subset_of_card_lt_finrankproof · cited by 0
- span_lt_top_of_card_lt_finrankproof · cited by 0