Theorems · Theorem · commutative algebra
IsAdjoinRoot.lift_self_apply
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {f : Polynomial R}
(h : IsAdjoinRoot S f) (x : S), (h.lift (algebraMap R S) h.root ⋯) x = x- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomproof · cited by 3,236
- IsAdjoinRootstatement and proof · cited by 61
- Polynomial.aeval_defproof · cited by 51
- IsAdjoinRoot.rootstatement and proof · cited by 34
- IsAdjoinRoot.mapproof · cited by 32
- IsAdjoinRoot.reprproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsAdjoinRoot.lift_selfproof · cited by 0