Theorems · Theorem · field theory
Polynomial.comp_assoc
∀ {R : Type u_1} [inst : CommSemiring R] (φ ψ χ : Polynomial R), (φ.comp ψ).comp χ = φ.comp (ψ.comp χ)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- pow_succproof · cited by 374
- Polynomial.compstatement and proof · cited by 193
- Polynomial.X_compproof · cited by 29
- Polynomial.mul_compproof · cited by 24
- Polynomial.induction_onproof · cited by 23
- Polynomial.add_compproof · cited by 20
- Polynomial.C_compproof · cited by 18
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.taylor_taylorproof · cited by 3
- Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_Xproof · cited by 3
- Polynomial.Chebyshev.S_eq_U_comp_half_mul_Xproof · cited by 3
- Polynomial.bernoulli_comp_one_sub_Xproof · cited by 2
- Polynomial.dvd_comp_C_mul_X_add_C_iffproof · cited by 2
- bernsteinPolynomial.flip'proof · cited by 2
- Polynomial.splits_iff_comp_splits_of_natDegree_eq_oneproof · cited by 1
- descPochhammer_eq_ascPochhammerproof · cited by 1
- Polynomial.dickson_one_one_mulproof · cited by 1
- Polynomial.rootMultiplicity_comp_C_mul_X_add_Cproof · cited by 1
- Polynomial.comp_neg_X_comp_neg_Xproof · cited by 0