Theorems · Theorem · field theory
Polynomial.natCast_mul_comp
∀ {R : Type u} [inst : Semiring R] {p r : Polynomial R} {n : ℕ}, (↑n * p).comp r = ↑n * p.comp r- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Polynomial.compstatement and proof · cited by 193
- Polynomial.C_eq_natCastproof · cited by 25
- Polynomial.C_mul_compproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eqproof · cited by 1
- Polynomial.mul_X_add_natCast_compproof · cited by 1
- Polynomial.mul_X_sub_intCast_compproof · cited by 1