Theorems · Theorem · commutative algebra
MvPolynomial.derivation_eq_of_forall_mem_vars
∀ {σ : Type u_1} {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
[inst_3 : Module (MvPolynomial σ R) A] {D₁ D₂ : Derivation R (MvPolynomial σ R) A} {f : MvPolynomial σ R},
(∀ i ∈ f.vars, D₁ (MvPolynomial.X i) = D₂ (MvPolynomial.X i)) → D₁ f = D₂ f- Defined in
- Mathlib.Algebra.MvPolynomial.Derivation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Modulestatement and proof · cited by 20,661
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Xstatement and proof · cited by 552
- Derivationstatement and proof · cited by 293
- MvPolynomial.varsstatement and proof · cited by 79
- MvPolynomial.mem_supported_varsproof · cited by 2
- MvPolynomial.derivation_eqOn_supportedproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.derivation_extproof · cited by 2
- MvPolynomial.derivation_eq_zero_of_forall_mem_varsproof · cited by 1