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Theorems · Theorem · field theory

Polynomial.derivative_C

∀ {R : Type u} [inst : Semiring R] {a : R}, Polynomial.derivative (Polynomial.C a) = 0
Defined in
Mathlib.Algebra.Polynomial.Derivative
Cited by
30 results in Mathlib
Foundations
Depth 106 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.derivative_one · cited by 17Polynomial.derivative_onePolynomial.derivative_natCast · cited by 6Polynomial.derivative_nat…Polynomial.derivative_eq_zero · cited by 4Polynomial.derivative_eq_…Polynomial.derivative_intCast · cited by 4Polynomial.derivative_int…Polynomial.derivative_of_natDegree_zero · cited by 4Polynomial.derivative_of_…Polynomial.derivative_X_sub_C · cited by 3Polynomial.derivative_X_s…Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succ · cited by 3Polynomial.card_roots_toF…Polynomial.derivative_comp · cited by 2Polynomial.derivative_compPolynomial.separable_C_mul_X_pow_add_C_mul_X_add_C · cited by 2Polynomial.separable_C_mu…Derivation.map_aeval · cited by 2Derivation.map_aevalPolynomial.derivative_X_add_C · cited by 2Polynomial.derivative_X_a…Polynomial.derivative_eval₂_C · cited by 1Polynomial.derivative_eva…Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative · cited by 1Polynomial.divByMonic_add…Lagrange.derivative_nodal · cited by 1Lagrange.derivative_nodalexists_derivative_mul_eq_and_isIntegral_coeff · cited by 1exists_derivative_mul_eq_…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapRingHom · cited by 10189RingHomPolynomial · cited by 5681Polynomialmul_one · cited by 3885mul_oneMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroNat.cast_zero · cited by 1870Nat.cast_zeroPolynomial.X · cited by 1639Polynomial.Xmap_zero · cited by 1614map_zeroPolynomial.C · cited by 1598Polynomial.Cmap_mul · cited by 1137map_mulpow_zero · cited by 1094pow_zeroPolynomial.derivative · cited by 331Polynomial.derivativePolynomial.derivative_CCITED BYCITES

Cites19

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

Cited by30

Results whose statement or proof uses this declaration.