Theorems · Theorem · field theory
Polynomial.C_mul
∀ {R : Type u} {a b : R} [inst : Semiring R], Polynomial.C (a * b) = Polynomial.C a * Polynomial.C b- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 101 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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement and proof · cited by 1,598
- RingHom.map_mulproof · cited by 45
Cited by35
Results whose statement or proof uses this declaration.
- minpoly.eq_of_irreducibleproof · cited by 8
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.Splits.of_natDegree_le_oneproof · cited by 4
- Polynomial.Splits.of_natDegree_le_one_of_invertibleproof · cited by 4
- Polynomial.isUnit_iff_degree_eq_zeroproof · cited by 3
- Polynomial.irreducible_of_monicproof · cited by 3
- WeierstrassCurve.C_Ψ₂Sqproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- Polynomial.associated_primPart_mulproof · cited by 2
- Cubic.C_mul_prod_X_sub_C_eqproof · cited by 2
- Polynomial.roots_C_mul_X_sub_C_of_IsUnitproof · cited by 2
- Polynomial.isCoprime_X_sub_C_of_isUnit_subproof · cited by 2