Theorems · Theorem · field theory
Cubic.discr_ne_zero_iff_roots_nodup
∀ {F : Type u_3} {K : Type u_4} {P : Cubic F} [inst : Field F] [inst_1 : Field K] {φ : F →+* K},
P.a ≠ 0 → (Polynomial.map φ P.toPoly).Splits → (P.discr ≠ 0 ↔ (Cubic.map φ P).roots.Nodup)- Defined in
- Mathlib.Algebra.CubicDiscriminant
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Multisetproof · cited by 2,627
- Polynomial.mapstatement and proof · cited by 806
- Multiset.consproof · cited by 313
- Polynomial.Splitsstatement and proof · cited by 290
- Multiset.Nodupstatement and proof · cited by 148
- Cubic.toPolystatement and proof · cited by 88
- Cubicstatement and proof · cited by 71
- Cubic.astatement and proof · cited by 46
- Multiset.mem_consproof · cited by 29
- Multiset.mem_singletonproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Cubic.card_roots_of_discr_ne_zeroproof · cited by 0