Theorems · Theorem · field theory
Algebraic.aleph0_le_cardinalMk_of_charZero
∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [CharZero A],
Cardinal.aleph0 ≤ Cardinal.mk { x // IsAlgebraic R x }- Defined in
- Mathlib.Algebra.AlgebraicCard
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- CharZerostatement and proof · cited by 932
- Cardinal.aleph0statement · cited by 521
- IsAlgebraicstatement · cited by 163
- Set.infinite_coe_iffproof · cited by 16
- Cardinal.infinite_iffproof · cited by 12
- Algebraic.infinite_of_charZeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebraic.cardinalMk_of_countable_of_charZeroproof · cited by 0