Theorems · Theorem · field theory
Subalgebra.inv_mem_of_algebraic
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (A : Subalgebra K L)
{x : ↥A}, IsAlgebraic K ↑x → (↑x)⁻¹ ∈ A- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- zero_addproof · cited by 2,366
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Subalgebrastatement and proof · cited by 1,353
- map_mulproof · cited by 1,137
- Polynomial.coeffproof · cited by 1,045
- Polynomial.aevalproof · cited by 615
- inv_zeroproof · cited by 184
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.isField_of_algebraicproof · cited by 0