Theorems · Theorem · field theory
Polynomial.mul_X_add_natCast_comp
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} {n : ℕ}, (p * (Polynomial.X + ↑n)).comp q = p.comp q * (q + ↑n)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- mul_addproof · cited by 413
- Polynomial.compstatement and proof · cited by 193
- Polynomial.add_compproof · cited by 20
- Nat.cast_commproof · cited by 16
- Polynomial.mul_X_compproof · cited by 5
- Polynomial.natCast_mul_compproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ascPochhammer_mulproof · cited by 0