Theorems · Theorem · commutative algebra
IsAdjoinRoot.aeval_root_self
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRoot S f), (Polynomial.aeval h.root) f = 0- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 112 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
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement · cited by 615
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.rootstatement · cited by 34
- IsAdjoinRoot.aeval_root_eq_mapproof · cited by 5
- IsAdjoinRoot.map_selfproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsAdjoinRootMonic.isIntegral_rootproof · cited by 1
- IsAdjoinRootMonic.minpoly_eqproof · cited by 1
- IsAdjoinRoot.lift_self_applystatement and proof · cited by 1
- IsAdjoinRoot.lift_selfstatement · cited by 0