Theorems · Theorem · field theory
Polynomial.sub_comp
∀ {R : Type u} [inst : Ring R] {p q r : Polynomial R}, (p - q).comp r = p.comp r - q.comp r- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Polynomial.compstatement · cited by 193
- Polynomial.eval₂_subproof · cited by 23
Cited by16
Results whose statement or proof uses this declaration.
- descPochhammer_succ_rightproof · cited by 14
- Polynomial.bernoulli_comp_one_add_Xproof · cited by 2
- Polynomial.Chebyshev.S_comp_two_mul_Xproof · cited by 2
- Polynomial.dvd_comp_C_mul_X_add_C_iffproof · cited by 2
- bernsteinPolynomial.flip'proof · cited by 2
- Polynomial.Chebyshev.C_comp_two_mul_Xproof · cited by 2
- Matrix.charpoly_sub_scalarproof · cited by 1
- X_pow_mul_sub_C_irreducibleproof · cited by 1
- Polynomial.mul_X_sub_intCast_compproof · cited by 1
- Polynomial.eval_divByMonic_eq_trailingCoeff_compproof · cited by 1
- Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eqproof · cited by 1
- splits_X_pow_sub_one_of_X_pow_sub_Cproof · cited by 1