Theorems · Theorem · number theory
FunctionField.finiteDimensional_ratFunc_of_constantExtension
∀ {F : Type u_1} (K : Type u_2) [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra (Polynomial F) K]
[inst_3 : FaithfulSMul (Polynomial F) K] [FunctionField F K] {E : Type u_3} [inst_5 : Field E] [inst_6 : Algebra F E]
[inst_7 : Algebra (Polynomial E) K] [FaithfulSMul (Polynomial E) K] [IsScalarTower (Polynomial F) (Polynomial E) K],
FiniteDimensional (RatFunc F) (RatFunc E)- Defined in
- Mathlib.NumberTheory.FunctionField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- IsScalarTowerstatement and proof · cited by 3,896
- FiniteDimensionalstatement · cited by 1,854
- LinearEquiv.symmproof · cited by 1,461
- FaithfulSMulstatement and proof · cited by 340
- RatFuncstatement and proof · cited by 301
- IsScalarTower.toAlgHomproof · cited by 232
- AlgEquiv.toLinearEquivproof · cited by 117
- Module.Finite.equivproof · cited by 20
- AlgEquiv.ofInjectiveFieldproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- FunctionField.finiteDimensional_of_constantExtensionproof · cited by 0