Theorems · Theorem · field theory
IntermediateField.isAlgebraic_adjoin_simple
∀ {K : Type u} [inst : Field K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] {x : L},
IsIntegral K x → Algebra.IsAlgebraic K ↥K⟮x⟯- Cited by
- 4 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalproof · cited by 1,854
- IntermediateFieldstatement · cited by 988
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement and proof · cited by 382
- Algebra.IsAlgebraicstatement · cited by 322
- IntermediateField.adjoin.finiteDimensionalproof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- RatFunc.transcendental_of_ne_Cproof · cited by 3
- IntermediateField.isAlgebraic_adjoinproof · cited by 2
- RatFunc.isAlgebraic_adjoin_simple_X'proof · cited by 0
- IntermediateField.AdjoinSimple.normal_algebraicClosureproof · cited by 0