Theorems · Theorem · field theory
Polynomial.sum_C_mul_X_pow_eq
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R), (p.sum fun n a => Polynomial.C a * Polynomial.X ^ n) = p- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 103 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.
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.sumstatement and proof · cited by 67
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
- Polynomial.sum_monomial_eqproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.induction_onproof · cited by 23
- Ideal.polynomial_mem_ideal_of_coeff_mem_idealproof · cited by 4
- Submodule.span_range_natDegree_eq_adjoinproof · cited by 3
- Polynomial.eval₂_algebraMap_Xproof · cited by 1
- mem_span_C_coeffproof · cited by 1
- PolyEquivTensor.left_invproof · cited by 0