Theorems · Theorem · commutative algebra
MvPolynomial.exists_finset_rename
∀ {σ : Type u_1} {R : Type u_4} [inst : CommSemiring R] (p : MvPolynomial σ R),
∃ s q, p = (MvPolynomial.rename Subtype.val) qEvery polynomial is a polynomial in finitely many variables.
- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 2 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.
Cites17
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
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- map_mulproof · cited by 1,137
- map_addproof · cited by 964
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.Cproof · cited by 400
- MvPolynomial.renamestatement and proof · cited by 168
- Finset.mem_insert_selfproof · cited by 128
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.exists_fin_renameproof · cited by 3
- MvPolynomial.exists_finset_rename₂proof · cited by 1