Theorems · Theorem · number theory
FunctionField.FiniteDimensional.adjoin_algebraMap_X
∀ {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], FiniteDimensional (↥F⟮(algebraMap (RatFunc F) K) RatFunc.X⟯) K- Defined in
- Mathlib.NumberTheory.FunctionField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- FiniteDimensionalstatement · cited by 1,854
- IntermediateFieldstatement · cited by 988
- nonZeroDivisorsstatement · cited by 895
- IntermediateField.adjoinstatement and proof · cited by 382
Cited by1
Results whose statement or proof uses this declaration.
- FunctionField.finiteDimensional_of_adjoin_transcendentalproof · cited by 0