Theorems · Theorem · field theory
Polynomial.sum_monomial_index
∀ {R : Type u} [inst : Semiring R] {S : Type u_1} [inst_1 : AddCommMonoid S] {n : ℕ} (a : R) (f : ℕ → R → S),
f n 0 = 0 → ((Polynomial.monomial n) a).sum f = f n a- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 97 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- Polynomial.monomialstatement · cited by 256
- Finsupp.sum_single_indexproof · cited by 130
- Polynomial.sumstatement · cited by 67
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.eval₂_monomialproof · cited by 19
- Polynomial.smeval_monomialproof · cited by 13
- Polynomial.derivative_monomialproof · cited by 8
- Polynomial.sum_C_indexproof · cited by 3
- Polynomial.sum_X_indexproof · cited by 2
- PolyEquivTensor.right_invproof · cited by 0
- Polynomial.hasseDeriv_compproof · cited by 0
- Polynomial.smeval_X_powproof · cited by 0