Theorems · Theorem · field theory
Polynomial.eq_C_of_natDegree_le_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.natDegree ≤ 0 → p = Polynomial.C (p.coeff 0)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.degree_le_of_natDegree_leproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.eq_C_of_natDegree_eq_zeroproof · cited by 22
- minpoly.unique'proof · cited by 4
- Polynomial.natDegree_pos_of_eval₂_rootproof · cited by 2
- minpoly.aeval_ne_zero_of_dvdNotUnit_minpolyproof · cited by 1
- Polynomial.hasseDeriv_natDegree_eq_Cproof · cited by 1
- Polynomial.exists_primitive_lcm_of_isPrimitiveproof · cited by 0