Theorems · Theorem · field theory
Polynomial.eq_C_of_degree_le_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.degree ≤ 0 → p = Polynomial.C (p.coeff 0)- Cited by
- 20 results in Mathlib
- Foundations
- Depth 102 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.
Cites14
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
- WithBotstatement · cited by 1,498
- Polynomial.coeffstatement and proof · cited by 1,045
- LE.le.trans_ltproof · cited by 795
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.extproof · cited by 118
- Polynomial.coeff_C_zeroproof · cited by 58
- WithBot.coe_lt_coeproof · cited by 55
Cited by20
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_add_Cproof · cited by 18
- Polynomial.degree_pos_of_irreducibleproof · cited by 10
- Polynomial.eq_C_of_degree_eq_zeroproof · cited by 9
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- Polynomial.eq_C_of_natDegree_le_zeroproof · cited by 6
- Polynomial.degree_le_zero_iffproof · cited by 5
- Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonnegproof · cited by 3
- Polynomial.isUnit_iff_degree_eq_zeroproof · cited by 3
- spectrum.map_polynomial_aeval_of_nonemptyproof · cited by 2
- Polynomial.isBoundedUnder_abs_atTop_iffproof · cited by 2
- Polynomial.degree_pos_of_not_isUnit_of_dvd_monicproof · cited by 2
- IsAlgClosed.roots_eq_zero_iffproof · cited by 1