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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
Assumes
CommSemiringCommSemiringAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.Bivariate.equivMvPolynomial_C_X · cited by 3Bivariate.equivMvPolynomi…Polynomial.Bivariate.equivMvPolynomial_X · cited by 3Bivariate.equivMvPolynomi…StandardEtalePair.lift_X · cited by 3StandardEtalePair.lift_XPolynomial.Bivariate.equivMvPolynomial_C_C · cited by 2Bivariate.equivMvPolynomi…Polynomial.Bivariate.aveal_eq_map_swap · cited by 1Bivariate.aveal_eq_map_sw…Polynomial.Bivariate.swap_C_C · cited by 1Bivariate.swap_C_CPolynomial.Bivariate.swap_Y · cited by 1Bivariate.swap_YPolynomial.aevalAeval_C · cited by 1Polynomial.aevalAeval_CPolynomial.Bivariate.aevalAeval_swap · cited by 0Bivariate.aevalAeval_swapPolynomial.coe_aevalAeval_eq_evalEval · cited by 0Polynomial.coe_aevalAeval…Polynomial.Bivariate.swap_C · cited by 0Bivariate.swap_CPolynomial.Bivariate.swap_X · cited by 0Bivariate.swap_XPolynomial.Bivariate.swap_map_C · cited by 0Bivariate.swap_map_CPolynomial.Bivariate.swap_monomial · cited by 0Bivariate.swap_monomialPolynomial.Bivariate.swap_monomial_monomial · cited by 0Bivariate.swap_monomial_m…DFunLike.coe · cited by 62936DFunLike.coeAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomEquiv · cited by 8337EquivPolynomial · cited by 5681PolynomialAlgHom · cited by 3236AlgHomPolynomial.C · cited by 1598Polynomial.CPolynomial.eval · cited by 796Polynomial.evalPolynomial.aeval · cited by 615Polynomial.aevalPolynomial.algebra · cited by 19Polynomial.algebraPolynomial.aevalAevalEquiv · cited by 3Polynomial.aevalAevalEquivPolynomial.aevalAevalEquiv_ap…CITED BYCITES

Cites12

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Cited by16

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