Theorems · Theorem · field theory
Polynomial.mul_comp
∀ {R : Type u_1} [inst : CommSemiring R] (p q r : Polynomial R), (p * q).comp r = p.comp r * q.comp r- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 102 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Polynomial.compstatement · cited by 193
- Polynomial.eval₂_mulproof · cited by 30
Cited by24
Results whose statement or proof uses this declaration.
- descPochhammer_succ_rightproof · cited by 14
- Polynomial.comp_assocproof · cited by 11
- ascPochhammer_succ_rightproof · cited by 11
- Polynomial.pow_compproof · cited by 7
- Polynomial.Chebyshev.S_eq_U_comp_half_mul_Xproof · cited by 3
- Polynomial.taylor_mulproof · cited by 3
- Polynomial.Splits.comp_of_natDegree_le_one_of_invertibleproof · cited by 3
- Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_Xproof · cited by 3
- Polynomial.bernoulli_comp_one_sub_Xproof · cited by 2
- Polynomial.Chebyshev.S_comp_two_mul_Xproof · cited by 2
- Polynomial.dvd_comp_C_mul_X_add_C_iffproof · cited by 2
- Polynomial.Chebyshev.C_comp_two_mul_Xproof · cited by 2