Theorems · Theorem · linear algebra
strongRankCondition_iff_forall_rank_lt_aleph0
∀ {R : Type u} [inst : Semiring R] [Nontrivial R],
StrongRankCondition R ↔ ∀ (n : ℕ), Module.rank R (Fin n → R) < Cardinal.aleph0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapproof · cited by 10,215
- Finsuppproof · cited by 5,255
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- Module.rankstatement and proof · cited by 496
Cited by1
Results whose statement or proof uses this declaration.
- strongRankCondition_iff_forall_zero_lt_finrankproof · cited by 0