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Theorems · Theorem · field theory

Polynomial.degree_C_le

∀ {R : Type u} {a : R} [inst : Semiring R], (Polynomial.C a).degree ≤ 0
Defined in
Mathlib.Algebra.Polynomial.Degree.Defs
Cited by
21 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.

Polynomial.degree_le_zero_iff · cited by 5Polynomial.degree_le_zero…Polynomial.degree_linear_le · cited by 5Polynomial.degree_linear_…Polynomial.monic_X_pow_add_C · cited by 3Polynomial.monic_X_pow_ad…Polynomial.card_nthRoots · cited by 3Polynomial.card_nthRootsspectrum.map_polynomial_aeval_of_degree_pos · cited by 2spectrum.map_polynomial_a…Polynomial.degree_X_add_C · cited by 2Polynomial.degree_X_add_CPolynomial.degree_X_pow_add_C · cited by 2Polynomial.degree_X_pow_a…Polynomial.degree_add_C · cited by 2Polynomial.degree_add_CPolynomial.tendsto_abv_eval₂_atTop · cited by 2Polynomial.tendsto_abv_ev…Polynomial.irreducible_C_mul_X_add_C · cited by 2Polynomial.irreducible_C_…Polynomial.mem_roots_sub_C · cited by 1Polynomial.mem_roots_sub_CPolynomial.degree_X_sub_C_le · cited by 1Polynomial.degree_X_sub_C…WittVector.RecursionMain.succNthDefiningPoly_degree · cited by 1RecursionMain.succNthDefi…Polynomial.degree_divX_lt · cited by 1Polynomial.degree_divX_ltPolynomial.mem_closure_X_union_C · cited by 1Polynomial.mem_closure_X_…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringRingHom · cited by 10189RingHomPolynomial · cited by 5681Polynomialle_refl · cited by 2061le_reflPolynomial.C · cited by 1598Polynomial.CWithBot · cited by 1498WithBotPolynomial.degree · cited by 643Polynomial.degreebot_le · cited by 306bot_lePolynomial.C_0 · cited by 40Polynomial.C_0Polynomial.degree_C · cited by 20Polynomial.degree_CPolynomial.degree_C_leCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.