Theorems · Theorem · field theory
IntermediateField.adjoin_simple_adjoin_simple
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α β : E),
IntermediateField.restrictScalars F (↥F⟮α⟯)⟮β⟯ = F⟮α, β⟯- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 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.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- IntermediateField.restrictScalarsstatement · cited by 66
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Field.exists_primitive_elementproof · cited by 6
- Field.exists_primitive_element_of_finite_intermediateFieldproof · cited by 1
- IntermediateField.isSeparable_adjoin_pair_of_isSeparableproof · cited by 0