Theorems · Theorem · field theory
Transcendental.infinite
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [Nontrivial R] {x : A},
Transcendental R x → Infinite A- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.aevalproof · cited by 615
- Infinitestatement · cited by 352
- Transcendentalstatement and proof · cited by 91
- Infinite.of_injectiveproof · cited by 10
- transcendental_iff_injectiveproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Transcendental.infiniteproof · cited by 1