Theorems · Theorem · field theory
FixedPoints.linearIndependent_smul_of_linearIndependent
∀ (G : Type u) [inst : Group G] (F : Type v) [inst_1 : Field F] [inst_2 : MulSemiringAction G F] {s : Finset F},
LinearIndepOn (↥(FixedPoints.subfield G F)) id ↑s → LinearIndepOn F ⇑(MulAction.toFun G F) ↑s- Defined in
- Mathlib.FieldTheory.Fixed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupFieldMulSemiringAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Set.imageproof · cited by 5,609
- Finsuppproof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
Cited by1
Results whose statement or proof uses this declaration.
- FixedPoints.rank_le_cardproof · cited by 1