Theorems · Theorem · field theory
FixedPoints.finrank_le_card
∀ (G : Type u) [inst : Group G] (F : Type v) [inst_1 : Field F] [inst_2 : MulSemiringAction G F] [inst_3 : Fintype G], Module.finrank (↥(FixedPoints.subfield G F)) F ≤ Fintype.card G
- Defined in
- Mathlib.FieldTheory.Fixed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 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.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- Cardinalproof · cited by 2,598
- Module.finrankstatement · cited by 1,770
- Fintype.cardstatement and proof · cited by 1,386
- MulSemiringActionstatement and proof · cited by 423
- Subfieldstatement · cited by 303
- Nat.cast_leproof · cited by 159
- Module.finrank_eq_rankproof · cited by 29
- FixedPoints.subfieldstatement and proof · cited by 20
- FixedPoints.rank_le_cardproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FixedPoints.finrank_eq_cardproof · cited by 3