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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
Cited by30
Results whose statement or proof uses this declaration.
- Polynomial.derivative_oneproof · cited by 17
- Polynomial.derivative_natCastproof · cited by 6
- Polynomial.derivative_eq_zeroproof · cited by 4
- Polynomial.derivative_intCastproof · cited by 4
- Polynomial.derivative_of_natDegree_zeroproof · cited by 4
- Polynomial.derivative_X_sub_Cproof · cited by 3
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3
- Polynomial.derivative_compproof · cited by 2
- Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_Cproof · cited by 2
- Derivation.map_aevalproof · cited by 2
- Polynomial.derivative_X_add_Cproof · cited by 2
- Polynomial.derivative_eval₂_Cproof · cited by 1