Theorems · Theorem · field theory
Algebraic.infinite_of_charZero
∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [CharZero A],
{x | IsAlgebraic R x}.Infinite- Defined in
- Mathlib.Algebra.AlgebraicCard
- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.ofPredstatement · cited by 6,101
- Nontrivialproof · cited by 2,416
- CharZerostatement and proof · cited by 932
- Set.Infinitestatement · cited by 263
- IsAlgebraicstatement · cited by 163
- Nat.cast_injectiveproof · cited by 39
- MulActionWithZero.nontrivialproof · cited by 3
- isAlgebraic_natCastproof · cited by 2
- Set.infinite_of_injective_forall_memproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Algebraic.aleph0_le_cardinalMk_of_charZeroproof · cited by 1