Theorems · Theorem · field theory
AlgebraicIndependent.matroid_isBasis_iff_of_subsingleton
∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[inst_3 : FaithfulSMul R A] [inst_4 : Subsingleton A] {s t : Set A},
(AlgebraicIndependent.matroid R A).IsBasis s t ↔ s = t- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Matroid.Eproof · cited by 550
- FaithfulSMulstatement and proof · cited by 340
- Matroid.IsBasisstatement · cited by 219
- Maximalproof · cited by 211
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- AlgebraicIndependent.matroidstatement and proof · cited by 17
- Function.Injective.subsingletonproof · cited by 16
- Subsingleton.to_noZeroDivisorsstatement · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.