Theorems · Theorem · field theory
algebraicIndependent_image
∀ {R : Type u_3} {A : Type u_5} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {ι : Type u_7}
{s : Set ι} {f : ι → A}, Set.InjOn f s → ((AlgebraicIndependent R fun x => f ↑x) ↔ AlgebraicIndependent R fun x => ↑x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Elemstatement · cited by 7,166
- Set.imagestatement · cited by 5,609
- Set.InjOnstatement and proof · cited by 543
- AlgebraicIndependentstatement · cited by 120
- Equiv.Set.imageOfInjOnproof · cited by 11
- algebraicIndependent_equiv'proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.of_compproof · cited by 2