Theorems · Theorem · field theory
Polynomial.degree_pos_of_irreducible
∀ {R : Type u} [inst : Field R] {p : Polynomial R}, Irreducible p → 0 < p.degree- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.coeffproof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Irreduciblestatement and proof · cited by 496
- lt_of_not_geproof · cited by 374
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.not_irreducible_Cproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.Splits.degree_eq_one_of_irreducibleproof · cited by 5
- Polynomial.separable_orproof · cited by 3
- X_pow_sub_C_irreducible_of_primeproof · cited by 2
- Irreducible.natDegree_le_twoproof · cited by 2
- FirstOrder.Field.isAlgClosed_of_model_ACFproof · cited by 2
- Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.natSepDegree_mul_eq_iffproof · cited by 1
- IsSepClosed.separableClosure_eq_bot_iffproof · cited by 1
- IsAlgClosed.algebraicClosure_eq_bot_iffproof · cited by 0
- IsAlgClosed.of_ringEquivproof · cited by 0