Theorems · Theorem · commutative algebra

MvPolynomial.X_mul_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} {s : σ},
  MvPolynomial.X s * p ∈ MvPolynomial.coeffsIn σ M ↔ p ∈ MvPolynomial.coeffsIn σ M

Defined in: Mathlib.Algebra.MvPolynomial.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring CommSemiring Module

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Modulestatement and proof · cited by 20,661
CommSemiringstatement and proof · cited by 10,911
Submodulestatement and proof · cited by 7,192
Finsuppstatement · cited by 5,255
mul_commproof · cited by 2,262
MvPolynomialstatement and proof · cited by 2,140
MvPolynomial.Xstatement and proof · cited by 552
MvPolynomial.coeffsInstatement and proof · cited by 18

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