Theorems · Theorem · number theory
FunctionField.finiteDimensional_of_adjoin_transcendental
∀ {F : Type u_3} {K : Type u_4} [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra (RatFunc F) K] [FunctionField F K]
[inst_4 : Algebra F K] [IsScalarTower F (RatFunc F) K] {y : K}, Transcendental F y → FiniteDimensional (↥F⟮y⟯) K- Defined in
- Mathlib.NumberTheory.FunctionField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Moduleproof · cited by 20,661
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- FiniteDimensionalstatement and proof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
- nonZeroDivisorsstatement · cited by 895
- IntermediateField.adjoinstatement and proof · cited by 382
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.