Theorems · Theorem · field theory
Infinite.nonempty_field
∀ {α : Type u} [Infinite α], Nonempty (Field α)Any infinite type can be endowed a field structure.
- Defined in
- Mathlib.FieldTheory.Cardinality
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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.
- Equivproof · cited by 8,337
- Fieldstatement · cited by 7,404
- Finsuppproof · cited by 5,255
- MvPolynomialproof · cited by 2,140
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0proof · cited by 521
- Infinitestatement and proof · cited by 352
- sup_of_le_leftproof · cited by 218
- FractionRingproof · cited by 200
- Cardinal.lift_idproof · cited by 163
- sup_of_le_rightproof · cited by 143
Cited by1
Results whose statement or proof uses this declaration.
- Field.nonempty_iffproof · cited by 0