Theorems · Theorem · field theory
Polynomial.aevalAevalEquiv_apply_apply
∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A] (xy : A × A) (x : Polynomial (Polynomial R)), ((Polynomial.aevalAevalEquiv R A) xy) x = Polynomial.eval xy.1 ((Polynomial.aeval (Polynomial.C xy.2)) x)
- Defined in
- Mathlib.Algebra.Polynomial.Bivariate
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 114 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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Equivstatement · cited by 8,337
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Cstatement · cited by 1,598
- Polynomial.evalstatement · cited by 796
- Polynomial.aevalstatement · cited by 615
- Polynomial.algebrastatement · cited by 19
- Polynomial.aevalAevalEquivstatement and proof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- Polynomial.Bivariate.equivMvPolynomial_C_Xproof · cited by 3
- Polynomial.Bivariate.equivMvPolynomial_Xproof · cited by 3
- StandardEtalePair.lift_Xproof · cited by 3
- Polynomial.Bivariate.equivMvPolynomial_C_Cproof · cited by 2
- Polynomial.Bivariate.aveal_eq_map_swapproof · cited by 1
- Polynomial.Bivariate.swap_C_Cproof · cited by 1
- Polynomial.Bivariate.swap_Yproof · cited by 1
- Polynomial.aevalAeval_Cproof · cited by 1
- Polynomial.Bivariate.aevalAeval_swapproof · cited by 0
- Polynomial.coe_aevalAeval_eq_evalEvalproof · cited by 0
- Polynomial.Bivariate.swap_Cproof · cited by 0
- Polynomial.Bivariate.swap_Xproof · cited by 0