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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.

MvPolynomial.exists_fin_rename · cited by 3MvPolynomial.exists_fin_r…MvPolynomial.exists_finset_rename · cited by 2MvPolynomial.exists_finse…MvPolynomial.rename_comp_rename · cited by 1MvPolynomial.rename_comp_…MvPolynomial.exists_finset_rename₂ · cited by 1MvPolynomial.exists_finse…Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial · cited by 1IsStandardSmoothOfRelativ…MvPolynomial.rename_leftInverse · cited by 1MvPolynomial.rename_leftI…MvPolynomial.totalDegree_renameEquiv · cited by 1MvPolynomial.totalDegree_…MvPolynomial.isIntegral_iff_isIntegral_coeff · cited by 1MvPolynomial.isIntegral_i…MvPolynomial.IsSymmetric.rename · cited by 1IsSymmetric.renameMvPolynomial.irreducible_mul_X_add · cited by 1MvPolynomial.irreducible_…MvPolynomial.isSymmetric_rename · cited by 0MvPolynomial.isSymmetric_…wittStructureInt_rename · cited by 0wittStructureInt_renameMvPolynomial.renameEquiv_trans · cited by 0MvPolynomial.renameEquiv_…DFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringFinsupp · cited by 5255FinsuppAlgHom · cited by 3236AlgHomMvPolynomial · cited by 2140MvPolynomialMvPolynomial.rename · cited by 168MvPolynomial.renameFinsupp.mapDomain.addMonoidHom · cited by 19mapDomain.addMonoidHomAddMonoidAlgebra.mapDomain · cited by 17AddMonoidAlgebra.mapDomainAddMonoidAlgebra.mapDomainAlgHom · cited by 13AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainAlgHom_apply · cited by 13AddMonoidAlgebra.mapDomai…Finsupp.mapDomain.addMonoidHom_comp · cited by 1mapDomain.addMonoidHom_co…AddMonoidAlgebra.mapDomainAlgHom_comp · cited by 1AddMonoidAlgebra.mapDomai…MvPolynomial.rename_renameCITED BYCITES

Cites12

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

Cited by13

Results whose statement or proof uses this declaration.