Theorems · Theorem · ring theory
SkewPolynomial.coeff_natCast_ite
∀ {R : Type u_1} {m n : ℕ} [inst : Semiring R] [MulSemiringAction (Multiplicative ℕ) R],
(↑m).coeff n = ↑(if n = 0 then m else 0)- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulSemiringAction
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.
- Semiringstatement and proof · cited by 13,802
- Nat.cast_zeroproof · cited by 1,870
- Multiplicativestatement and proof · cited by 875
- MulSemiringActionstatement and proof · cited by 423
- SkewPolynomialstatement · cited by 124
- SkewPolynomial.coeffstatement and proof · cited by 37
- Nat.cast_iteproof · cited by 16
- SkewPolynomial.coeff_Cproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- SkewPolynomial.coeff_ofNat_succproof · cited by 0
- SkewPolynomial.coeff_ofNat_zeroproof · cited by 0