Theorems · Theorem · field theory
Polynomial.rootMultiplicity_X_sub_C
∀ {R : Type u} [inst : CommRing R] [Nontrivial R] [inst_2 : DecidableEq R] {x y : R},
Polynomial.rootMultiplicity x (Polynomial.X - Polynomial.C y) = if x = y then 1 else 0- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- Polynomial.rootMultiplicity_eq_zeroproof · cited by 6
- Polynomial.root_X_sub_Cproof · cited by 1
- Polynomial.rootMultiplicity_X_sub_C_selfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.roots_X_sub_Cproof · cited by 14