Theorems · Theorem · field theory
Polynomial.eval_mul_X
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {x : R},
Polynomial.eval x (p * Polynomial.X) = Polynomial.eval x p * x- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂_mul_Xproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- descPochhammer_eval_eq_ascPochhammerproof · cited by 4
- descPochhammer_eval_eq_descFactorialproof · cited by 3
- ascPochhammer_eval_zeroproof · cited by 3
- descPochhammer_succ_evalproof · cited by 3
- ascPochhammer_posproof · cited by 3
- ascPochhammer_succ_evalproof · cited by 3
- Polynomial.eval_mul_X_sub_Cproof · cited by 2
- eval_det_add_X_smulproof · cited by 2
- Polynomial.eval_mul_X_powproof · cited by 1
- Matrix.det_one_add_smulproof · cited by 1
- descPochhammer_eval_zeroproof · cited by 1