Theorems · Theorem · field theory

AlgebraicIndependent.sumElim

∀ {ι : Type u_1} {R : Type u_3} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A]
  [inst_2 : Algebra R A],
  AlgebraicIndependent R x →
    ∀ {ι' : Type u_4} {y : ι' → A},
      AlgebraicIndependent (↥(Algebra.adjoin R (Set.range x))) y → AlgebraicIndependent R (Sum.elim y x)

Defined in: Mathlib.RingTheory.AlgebraicIndependent.Transcendental
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Set.rangestatement and proof · cited by 4,705
Subalgebrastatement · cited by 1,353
Algebra.adjoinstatement and proof · cited by 535
AlgebraicIndependentstatement and proof · cited by 120
AlgebraicIndependent.sumElim_iffproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicIndependent.sumElim_of_towerproof · cited by 1