Theorems · Theorem · commutative algebra
MvPolynomial.exists_fin_rename
∀ {σ : Type u_1} {R : Type u_4} [inst : CommSemiring R] (p : MvPolynomial σ R),
∃ n f, ∃ (_ : Function.Injective f), ∃ q, p = (MvPolynomial.rename f) qEvery polynomial is a polynomial in finitely many variables.
- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 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.
Cites16
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
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Equivproof · cited by 8,337
- Finsuppstatement · cited by 5,255
- Equiv.symmproof · cited by 3,681
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Fintype.cardproof · cited by 1,386
- Equiv.injectiveproof · cited by 464
- Equiv.symm_apply_applyproof · cited by 320
- Subtype.val_injectiveproof · cited by 232
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_cardproof · cited by 3
- MvPolynomial.funext_setproof · cited by 2
- MvPolynomial.isNilpotent_iffproof · cited by 0