Theorems · Theorem · field theory
Polynomial.coeff_add
∀ {R : Type u} [inst : Semiring R] (p q : Polynomial R) (n : ℕ), (p + q).coeff n = p.coeff n + q.coeff n- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 77 results in Mathlib
- Foundations
- Depth 85 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.
Cites8
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.coeffstatement and proof · cited by 1,045
- AddMonoidAlgebraproof · cited by 649
- Equiv.toFunproof · cited by 279
- AddMonoidAlgebra.coeffEquivproof · cited by 22
- Polynomial.casesOnproof · cited by 15
- Finsupp.add_applyproof · cited by 11
Cited by78
Results whose statement or proof uses this declaration.
- Polynomial.degree_add_eq_left_of_degree_ltproof · cited by 14
- Polynomial.lcoeffproof · cited by 11
- Polynomial.leadingCoeff_add_of_degree_ltproof · cited by 10
- MvPolynomial.optionEquivLeft_coeff_some_coeff_noneproof · cited by 7
- Polynomial.coeff_freeMonicproof · cited by 6
- Polynomial.divX_mul_X_addproof · cited by 6
- Ideal.mem_map_C_iffproof · cited by 6
- MvPolynomial.finSuccEquiv_coeff_coeffproof · cited by 5
- Polynomial.eq_X_add_C_of_degree_le_oneproof · cited by 5
- matPolyEquiv_coeff_applyproof · cited by 5
- Polynomial.reflect_addproof · cited by 5
- Polynomial.Splits.of_natDegree_le_one_of_invertibleproof · cited by 4