Theorems · Theorem · field theory
Cubic.card_roots_le
∀ {R : Type u_1} {P : Cubic R} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : DecidableEq R],
P.roots.toFinset.card ≤ 3- Defined in
- Mathlib.Algebra.CubicDiscriminant
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LE.le.transproof · cited by 3,151
- Finset.cardstatement · cited by 2,327
- IsDomainstatement and proof · cited by 2,196
- Multiset.cardproof · cited by 375
- Polynomial.rootsproof · cited by 264
- Multiset.toFinsetstatement · cited by 230
- Cubic.toPolyproof · cited by 88
- WithBot.coe_le_coeproof · cited by 76
- Cubicstatement and proof · cited by 71
- Polynomial.roots.congr_simpproof · cited by 31
- Polynomial.roots_zeroproof · cited by 19
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