Theorems · Theorem · field theory
InfiniteGalois.mem_bot_iff_fixed
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] [IsGalois k K] (x : K),
x ∈ ⊥ ↔ ∀ (f : Gal(K/k)), f x = x- Defined in
- Mathlib.FieldTheory.Galois.Infinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Algebrastatement and proof · cited by 11,388
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement · cited by 4,720
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- IsGaloisstatement and proof · cited by 149
Cited by1
Results whose statement or proof uses this declaration.
- InfiniteGalois.mem_range_algebraMap_iff_fixedproof · cited by 0