Theorems · Theorem · field theory
FixedBy.subfield_mem_iff
∀ {M : Type u} [inst : Monoid M] (F : Type v) [inst_1 : Field F] [inst_2 : MulSemiringAction M F] (m : M) (x : F),
x ∈ FixedBy.subfield F m ↔ m • x = x- Defined in
- Mathlib.FieldTheory.Fixed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidFieldMulSemiringAction
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Monoidstatement and proof · cited by 3,887
- MulSemiringActionstatement and proof · cited by 423
- Subfieldstatement · cited by 303
- FixedBy.subfieldstatement · cited by 1
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