Theorems · Theorem · number theory
FiniteField.even_card_iff_char_two
∀ {F : Type u_3} [inst : Field F] [inst_1 : Fintype F], ringChar F = 2 ↔ Fintype.card F % 2 = 0The finite field F has even cardinality iff it has characteristic 2.
- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 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.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Nat.Primeproof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- PNatproof · cited by 392
- PNat.valproof · cited by 226
- ringCharstatement and proof · cited by 73
- FiniteField.cardproof · cited by 10
- Nat.even_iffproof · cited by 8
- Nat.Prime.even_iffproof · cited by 2
- Nat.even_powproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- FiniteField.odd_card_of_char_ne_twoproof · cited by 6
- FiniteField.even_card_of_char_twoproof · cited by 3