Theorems · Theorem · field theory

Polynomial.leadingCoeff_cubic

∀ {R : Type u} {a b c d : R} [inst : Semiring R],
  a ≠ 0 →
    (Polynomial.C a * Polynomial.X ^ 3 + Polynomial.C b * Polynomial.X ^ 2 + Polynomial.C c * Polynomial.X +
          Polynomial.C d).leadingCoeff =
      a

Defined in: Mathlib.Algebra.Polynomial.Degree.SmallDegree
Cited by: 1 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · 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 and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
add_commproof · cited by 1,535
add_assocproof · cited by 746
Polynomial.leadingCoeffstatement and proof · cited by 498
Polynomial.leadingCoeff_add_of_degree_ltproof · cited by 10
Polynomial.leadingCoeff_C_mul_X_powproof · cited by 4
Polynomial.degree_quadratic_lt_degree_C_mul_X_cbproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Cubic.leadingCoeff_of_a_ne_zeroproof · cited by 3