Theorems · Theorem · commutative algebra
MvPolynomial.aeval_rename
∀ {σ : Type u_1} {τ : Type u_2} {R : Type u_4} {S : Type u_5} [inst : CommSemiring R] [inst_1 : CommSemiring S]
(k : σ → τ) (g : τ → S) (p : MvPolynomial σ R) [inst_2 : Algebra R S],
(MvPolynomial.aeval g) ((MvPolynomial.rename k) p) = (MvPolynomial.aeval (g ∘ k)) p- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.aevalstatement · cited by 298
- MvPolynomial.renamestatement · cited by 168
- MvPolynomial.eval₂Hom_renameproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.compproof · cited by 9
- Algebra.Generators.toAlgHom_ofComp_surjectiveproof · cited by 5
- Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toCompproof · cited by 3
- AlgebraicIndependent.mapproof · cited by 3
- PolynomialLaw.isCompat_applyproof · cited by 2
- MvPolynomial.exists_restrict_to_varsproof · cited by 1
- MvPolynomial.aeval_id_renameproof · cited by 1
- MvPolynomial.aeval_comp_renameproof · cited by 0
- Algebra.Generators.toAlgHom_ofComp_localizationAwayproof · cited by 0