Theorems · Theorem · commutative algebra
Subalgebra.aeval_coe
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
(S : Subalgebra R A) (x : ↥S) (p : Polynomial R), (Polynomial.aeval ↑x) p = ↑((Polynomial.aeval x) p)- Defined in
- Mathlib.RingTheory.Polynomial.Tower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- Polynomial.aevalstatement · cited by 615
- Polynomial.aeval_algebraMap_applyproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.inv_mem_of_algebraicproof · cited by 1
- Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zeroproof · cited by 1