Theorems · Theorem · field theory
Polynomial.coeff_mul_add_eq_of_natDegree_le
∀ {R : Type u} [inst : Semiring R] {df dg : ℕ} {f g : Polynomial R},
f.natDegree ≤ df → g.natDegree ≤ dg → (f * g).coeff (df + dg) = f.coeff df * g.coeff dg- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
Cites14
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- LE.le.trans_ltproof · cited by 795
- Finset.HasAntidiagonal.antidiagonalproof · cited by 218
- lt_or_geproof · cited by 182
- Polynomial.coeff_eq_zero_of_natDegree_ltproof · cited by 55
- Finset.HasAntidiagonal.mem_antidiagonalproof · cited by 51
- Finset.sum_eq_single_of_memproof · cited by 33
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.coeff_list_prod_of_natDegree_leproof · cited by 1
- Polynomial.coeff_pow_of_natDegree_leproof · cited by 1