Theorems · Theorem · field theory
Cubic.card_roots_of_discr_ne_zero
∀ {F : Type u_3} {K : Type u_4} {P : Cubic F} [inst : Field F] [inst_1 : Field K] {φ : F →+* K}
[inst_2 : DecidableEq K],
P.a ≠ 0 → (Polynomial.map φ P.toPoly).Splits → P.discr ≠ 0 → (Cubic.map φ P).roots.toFinset.card = 3- Defined in
- Mathlib.Algebra.CubicDiscriminant
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFieldDecidableEq
Around this declaration
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Cites15
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
- Finset.cardstatement · cited by 2,327
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Splitsstatement and proof · cited by 290
- Multiset.toFinsetstatement · cited by 230
- Cubic.toPolystatement and proof · cited by 88
- Cubicstatement and proof · cited by 71
- Cubic.astatement and proof · cited by 46
- Cubic.rootsstatement · cited by 14
- Cubic.mapstatement · cited by 13
- Cubic.discrstatement and proof · cited by 10
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