Theorems · Theorem · field theory
Polynomial.smeval_sub
∀ (R : Type u_1) [inst : Ring R] {S : Type u_2} [inst_1 : AddCommGroup S] [inst_2 : Pow S ℕ] [inst_3 : Module R S]
(p q : Polynomial R) (x : S), (p - q).smeval x = p.smeval x - q.smeval x- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupPowModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- sub_eq_add_negproof · cited by 1,023
- Polynomial.smevalstatement and proof · cited by 65
- Polynomial.smeval_addproof · cited by 22
- Polynomial.smeval_negproof · cited by 2
Cited by6
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.descPochhammer_succ_succ_smevalproof · cited by 1
- Ring.descPochhammer_smeval_addproof · cited by 1
- Polynomial.descPochhammer_smeval_eq_descFactorialproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1