Theorems · Theorem · field theory
IntermediateField.sup_toSubalgebra_of_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) [FiniteDimensional K ↥E1], (E1 ⊔ E2).toSubalgebra = E1.toSubalgebra ⊔ E2.toSubalgebra- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- FiniteDimensionalstatement and proof · cited by 1,854
- Subalgebrastatement · cited by 1,353
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.toSubalgebrastatement · cited by 134
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_leftproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.isCyclotomicExtension_lcm_supproof · cited by 2
- IntermediateField.finrank_sup_leproof · cited by 0
- IntermediateField.LinearDisjoint.of_finrank_supproof · cited by 0