Theorems · Theorem · field theory
Cubic.leadingCoeff_of_c_eq_zero
∀ {R : Type u_1} {P : Cubic R} [inst : Semiring R], P.a = 0 → P.b = 0 → P.c = 0 → P.toPoly.leadingCoeff = P.d- Defined in
- Mathlib.Algebra.CubicDiscriminant
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 108 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.
Cites11
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
- Polynomialproof · cited by 5,681
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Cubic.toPolystatement · cited by 88
- Cubicstatement and proof · cited by 71
- Cubic.astatement and proof · cited by 46
- Polynomial.leadingCoeff_Cproof · cited by 39
- Cubic.bstatement and proof · cited by 32
- Cubic.cstatement and proof · cited by 26
- Cubic.dstatement and proof · cited by 21
- Cubic.of_c_eq_zeroproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Cubic.monic_of_d_eq_oneproof · cited by 1
- Cubic.leadingCoeff_of_c_eq_zero'proof · cited by 0