Theorems · Theorem · field theory
AlgebraicIndependent.linearIndependent
∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A],
AlgebraicIndependent R x → LinearIndependent R x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- Finsuppproof · cited by 5,255
- LinearMap.compproof · cited by 1,642
- one_smulproof · cited by 1,374
- LinearIndependentstatement · cited by 560
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.aevalproof · cited by 298
- Finsupp.linearCombinationproof · cited by 269
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.injectiveproof · cited by 11
- AlgebraicIndependent.ne_zeroproof · cited by 0