Theorems · Theorem · field theory
Polynomial.coeff_natCast_ite
∀ {R : Type u} {m n : ℕ} [inst : Semiring R], (↑m).coeff n = ↑(if n = 0 then m else 0)- 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.
Cites6
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 · cited by 5,681
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.coeff_Cproof · cited by 33
- Nat.cast_iteproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- WeierstrassCurve.coeff_Ψ₃proof · cited by 2
- WeierstrassCurve.coeff_preΨ₄proof · cited by 2
- Polynomial.intCast_coeff_zeroproof · cited by 1
- Polynomial.coeff_ofNat_succproof · cited by 0
- Polynomial.natCast_coeff_zeroproof · cited by 0
- Polynomial.natCast_injproof · cited by 0