Theorems · Theorem · field theory
IntermediateField.isAlgebraic_iSup
∀ {K : Type u} [inst : Field K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] {ι : Type u_4}
{t : ι → IntermediateField K L}, (∀ (i : ι), Algebra.IsAlgebraic K ↥(t i)) → Algebra.IsAlgebraic K ↥(⨆ i, t i)A compositum of algebraic extensions is algebraic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 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.
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- iSupstatement and proof · cited by 2,415
- FiniteDimensionalproof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicstatement and proof · cited by 322
- IsAlgebraicproof · cited by 163
- Algebra.IsIntegral.isIntegralproof · cited by 86
- Subtype.coe_mkproof · cited by 81
- IntermediateField.adjoin.finiteDimensionalproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.isAlgebraic_adjoinproof · cited by 2