Theorems · Theorem · field theory
Polynomial.sum_C_index
∀ {R : Type u} [inst : Semiring R] {a : R} {β : Type u_1} [inst_1 : AddCommMonoid β] {f : ℕ → R → β},
f 0 0 = 0 → (Polynomial.C a).sum f = f 0 a- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoid
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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.sumstatement · cited by 67
- Polynomial.sum_monomial_indexproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.eval₂_Cproof · cited by 50
- Polynomial.derivative_Cproof · cited by 30
- Polynomial.smeval_Cproof · cited by 8