Theorems · Theorem · field theory
Polynomial.irreducible_of_degree_le_three_of_not_isRoot
∀ {K : Type u_1} [inst : Field K] {p : Polynomial K},
p.natDegree ∈ Finset.Icc 1 3 → (∀ (x : K), ¬p.IsRoot x) → Irreducible p- Cited by
- 0 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Nat.cast_oneproof · cited by 2,501
- le_antisymmproof · cited by 2,068
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.degreeproof · cited by 643
- Irreduciblestatement · cited by 496
- Finset.Iccstatement and proof · cited by 348
- not_leproof · cited by 328
- Polynomial.IsRootstatement and proof · cited by 152
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