Theorems · Theorem · field theory
Polynomial.mul_coeff_one
∀ {R : Type u} [inst : Semiring R] (p q : Polynomial R), (p * q).coeff 1 = p.coeff 0 * q.coeff 1 + p.coeff 1 * q.coeff 0- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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
- Finsetproof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Finset.rangeproof · cited by 1,341
- Polynomial.coeffstatement and proof · cited by 1,045
- Finset.sum_singletonproof · cited by 251
- tsub_selfproof · cited by 154
- tsub_zeroproof · cited by 123
- Finset.sum_range_succproof · cited by 121
- Finset.sum_mapproof · cited by 115
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Monic.nextCoeff_mulproof · cited by 3