Theorems · Theorem · field theory
Polynomial.monic_X_add_C
∀ {R : Type u} [inst : Semiring R] (x : R), (Polynomial.X + Polynomial.C x).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 108 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.
Cites10
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 · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- pow_oneproof · cited by 894
- one_ne_zeroproof · cited by 885
- Polynomial.Monicstatement · cited by 461
- Polynomial.monic_X_pow_add_Cproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.Monic.comp_X_add_Cproof · cited by 3
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- cyclotomic_prime_pow_comp_X_add_one_isEisensteinAtproof · cited by 1
- Polynomial.Splits.scaleRootsproof · cited by 1
- Polynomial.natDegree_pow_X_add_Cproof · cited by 1
- Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeffproof · cited by 1
- Polynomial.not_isUnit_X_add_Cproof · cited by 0
- Polynomial.Splits.comp_X_add_Cproof · cited by 0