Theorems · Theorem · field theory
Polynomial.smeval_mul
∀ (R : Type u_1) [inst : Semiring R] (p q : Polynomial R) {S : Type u_2} [inst_1 : NonAssocSemiring S]
[inst_2 : Module R S] [inst_3 : Pow S ℕ] (x : S) [NatPowAssoc S] [IsScalarTower R S S] [SMulCommClass R S S],
(p * q).smeval x = p.smeval x * q.smeval x- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- NonAssocSemiringstatement and proof · cited by 805
- add_mulproof · cited by 363
- smul_mul_assocproof · cited by 77
- Polynomial.smevalstatement and proof · cited by 65
- NatPowAssocstatement and proof · cited by 53
- Polynomial.induction_on'proof · cited by 50
- Polynomial.smeval_addproof · cited by 22
Cited by9
Results whose statement or proof uses this declaration.
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1
- Polynomial.descPochhammer_smeval_eq_descFactorialproof · cited by 1
- Ring.descPochhammer_smeval_addproof · cited by 1
- Ring.descPochhammer_succ_succ_smevalproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1