Theorems · Inductive type · ring theory
RankCondition
(R : Type u) → [Semiring R] → Prop
We say that R satisfies the rank condition if (Fin n → R) →ₗ[R] (Fin m → R) surjective
implies m ≤ n.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
Cited by17
Results whose statement or proof uses this declaration.
- le_of_fin_surjectivestatement and proof · cited by 2
- Module.Basis.mk_eq_spanRankstatement and proof · cited by 1
- Basis.le_span''statement and proof · cited by 1
- card_le_of_surjectivestatement and proof · cited by 1
- card_le_of_surjective'statement and proof · cited by 1
- Module.Basis.le_spanstatement and proof · cited by 1
- RankCondition.casesOnstatement and proof · cited by 1
- RankCondition.le_of_fin_surjectivestatement and proof · cited by 1
- Submodule.spanRank_span_of_linearIndepOnstatement and proof · cited by 1
- Submodule.spanRank_span_range_of_linearIndependentstatement and proof · cited by 1
- rankCondition_iffstatement and proof · cited by 1
- basis_le_span'statement and proof · cited by 1