Theorems · Theorem · field theory
Polynomial.root_X_sub_C
∀ {R : Type u} {a b : R} [inst : Ring R], (Polynomial.X - Polynomial.C a).IsRoot b ↔ a = b- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.evalproof · cited by 796
- sub_eq_zeroproof · cited by 407
- Polynomial.eval_Xproof · cited by 172
- Polynomial.IsRootstatement · cited by 152
- Polynomial.eval_Cproof · cited by 145
- Polynomial.eval_subproof · cited by 124
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicity_X_sub_Cproof · cited by 1