Theorems · Theorem · field theory
Polynomial.smeval_commute_left
∀ (R : Type u_1) [inst : Semiring R] (p : Polynomial R) {S : Type u_2} [inst_1 : Semiring S] [inst_2 : Module R S]
[IsScalarTower R S S] [SMulCommClass R S S] {x y : S}, Commute x y → Commute (p.smeval x) y- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Commutestatement and proof · cited by 639
- Polynomial.smevalstatement and proof · cited by 65
- Polynomial.induction_on'proof · cited by 50
- Polynomial.smeval_addproof · cited by 22
- Polynomial.smeval_monomialproof · cited by 13
- Commute.smul_leftproof · cited by 11
- Commute.add_leftproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.smeval_commuteproof · cited by 1