Theorems · Theorem · commutative algebra
MvPolynomial.adjoin_range_X
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R], Algebra.adjoin R (Set.range MvPolynomial.X) = ⊤- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Finsuppstatement · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- MvPolynomialstatement and proof · cited by 2,140
- Subalgebrastatement and proof · cited by 1,353
- MvPolynomial.Xstatement and proof · cited by 552
- Algebra.adjoinstatement and proof · cited by 535
- Set.mem_range_selfproof · cited by 328
- Algebra.subset_adjoinproof · cited by 109
- top_uniqueproof · cited by 102
- MvPolynomial.induction_onproof · cited by 43
Cited by4
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.mvPolynomialproof · cited by 3
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Algebra.FinitePresentation.ker_fg_of_mvPolynomialproof · cited by 1
- DividedPowerAlgebra.lift_surjectiveproof · cited by 0