Theorems · Theorem · commutative algebra
MvPolynomial.C_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} {x : S}, MvPolynomial.C x ∈ MvPolynomial.coeffsIn σ M ↔ x ∈ M- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.Cstatement · cited by 400
- MvPolynomial.coeffsInstatement · cited by 18
- MvPolynomial.monomial_mem_coeffsInproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.one_coeffsInproof · cited by 0