Theorems · Theorem · field theory
Polynomial.coeff_X_sub_C_mul
∀ {R : Type u} [inst : Ring R] {p : Polynomial R} {r : R} {a : ℕ},
((Polynomial.X - Polynomial.C r) * p).coeff (a + 1) = p.coeff a - r * p.coeff (a + 1)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- sub_mulproof · cited by 170
- Polynomial.coeff_C_mulproof · cited by 55
- Polynomial.coeff_subproof · cited by 49
- Polynomial.coeff_X_mulproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.succ_signVariations_le_X_sub_C_mulproof · cited by 1
- Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zeroproof · cited by 1