Theorems · Theorem · field theory
IntermediateField.sup_toSubalgebra_of_isAlgebraic_left
∀ {K : Type u_3} {L : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
(E1 E2 : IntermediateField K L) [Algebra.IsAlgebraic K ↥E1],
(E1 ⊔ E2).toSubalgebra = E1.toSubalgebra ⊔ E2.toSubalgebra- Cited by
- 2 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Subalgebrastatement and proof · cited by 1,353
- IntermediateFieldstatement and proof · cited by 988
- Algebra.IsAlgebraicstatement and proof · cited by 322
- sup_commproof · cited by 165
- IntermediateField.toSubalgebrastatement and proof · cited by 134
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.sup_toSubalgebra_of_isAlgebraicproof · cited by 3
- IntermediateField.sup_toSubalgebra_of_leftproof · cited by 3