Theorems · Theorem · commutative algebra
MvPolynomial.mul_monomial_mem_coeffsIn
∀ {R : Type u_2} {S : Type u_3} {σ : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Module R S]
{M : Submodule R S} {p : MvPolynomial σ S} {i : σ →₀ ℕ},
p * (MvPolynomial.monomial i) 1 ∈ MvPolynomial.coeffsIn σ M ↔ p ∈ MvPolynomial.coeffsIn σ M- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.monomialstatement · cited by 253
- add_tsub_cancel_rightproof · cited by 172
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.mul_X_mem_coeffsInproof · cited by 0