Theorems · Theorem · field theory
Polynomial.smeval_comp
∀ (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.comp q).smeval x = p.smeval (q.smeval x)- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Polynomial.compstatement and proof · cited by 193
- 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
- Polynomial.add_compproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.descPochhammer_succ_succ_smevalproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1