Theorems · Theorem · field theory
IntermediateField.finiteDimensional_adjoin_pair
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {x y : L},
IsIntegral K x → IsIntegral K y → FiniteDimensional K ↥K⟮x, y⟯- Cited by
- 2 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement and proof · cited by 382
- Set.singleton_unionproof · cited by 22
- IntermediateField.adjoin.finiteDimensionalproof · cited by 21
- IntermediateField.adjoin_unionproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- isNonarchimedean_spectralNormproof · cited by 1
- spectralNorm_mulproof · cited by 0