Theorems · Theorem · commutative algebra
MvPolynomial.exists_rename_eq_of_vars_subset_range
∀ {R : Type u} {σ : Type u_1} {τ : Type u_2} [inst : CommSemiring R] (p : MvPolynomial σ R) (f : τ → σ),
Function.Injective f → ↑p.vars ⊆ Set.range f → ∃ q, (MvPolynomial.rename f) q = p- Defined in
- Mathlib.Algebra.MvPolynomial.Variables
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 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.
Cites23
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
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Finsuppstatement · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.Cproof · cited by 400
- RingHom.extproof · cited by 331
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.mem_supportedproof · cited by 4
- MvPolynomial.irreducible_mul_X_addproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1