Theorems · Theorem · field theory
Polynomial.smeval_add
∀ (R : Type u_1) [inst : Semiring R] (p q : Polynomial R) {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ]
[inst_3 : Module R S] (x : S), (p + q).smeval x = p.smeval x + q.smeval x- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommMonoidstatement and proof · cited by 12,281
- Polynomialstatement and proof · cited by 5,681
- zero_smulproof · cited by 716
- add_smulproof · cited by 204
- Polynomial.smevalstatement · cited by 65
- Polynomial.smul_powproof · cited by 9
- Polynomial.smeval_eq_sumproof · cited by 9
- Polynomial.sum_add_indexproof · cited by 3
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.smeval_mulproof · cited by 9
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Polynomial.smeval_subproof · cited by 6
- Polynomial.smeval_compproof · cited by 5
- Polynomial.smeval_natCastproof · cited by 4
- Polynomial.ascPochhammer_smeval_castproof · cited by 3
- Polynomial.smeval_C_mulproof · cited by 3
- Polynomial.smeval_mul_Xproof · cited by 2
- Polynomial.smeval_negproof · cited by 2
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1