Theorems · Theorem · field theory
IntermediateField.mem_adjoin_range_iff
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {ι : Type u_3} (i : ι → E)
(x : E), x ∈ IntermediateField.adjoin F (Set.range i) ↔ ∃ r s, x = (MvPolynomial.aeval i) r / (MvPolynomial.aeval i) s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Finsuppstatement · cited by 5,255
- Set.rangestatement · cited by 4,705
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- MvPolynomial.aevalstatement and proof · cited by 298
- Algebra.adjoin_range_eq_range_aevalproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.mem_adjoin_iffproof · cited by 0