Theorems · Theorem · commutative algebra
MvPolynomial.rename_rename
∀ {σ : Type u_1} {τ : Type u_2} {α : Type u_3} {R : Type u_4} [inst : CommSemiring R] (f : σ → τ) (g : τ → α)
(p : MvPolynomial σ R), (MvPolynomial.rename g) ((MvPolynomial.rename f) p) = (MvPolynomial.rename (g ∘ f)) p- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 89 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.
Cites12
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
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.renamestatement · cited by 168
- Finsupp.mapDomain.addMonoidHomproof · cited by 19
- AddMonoidAlgebra.mapDomainproof · cited by 17
- AddMonoidAlgebra.mapDomainAlgHomproof · cited by 13
- AddMonoidAlgebra.mapDomainAlgHom_applyproof · cited by 13
- Finsupp.mapDomain.addMonoidHom_compproof · cited by 1
- AddMonoidAlgebra.mapDomainAlgHom_compproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- MvPolynomial.exists_fin_renameproof · cited by 3
- MvPolynomial.exists_finset_renameproof · cited by 2
- MvPolynomial.rename_comp_renameproof · cited by 1
- MvPolynomial.exists_finset_rename₂proof · cited by 1
- Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomialproof · cited by 1
- MvPolynomial.rename_leftInverseproof · cited by 1
- MvPolynomial.totalDegree_renameEquivproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- MvPolynomial.IsSymmetric.renameproof · cited by 1
- MvPolynomial.irreducible_mul_X_addproof · cited by 1
- MvPolynomial.isSymmetric_renameproof · cited by 0
- wittStructureInt_renameproof · cited by 0