Theorems · Theorem · field theory
IsPerfectClosure.equiv_comp_equiv_apply_eq_self
∀ {K : Type u_1} {L : Type u_2} {M : Type u_3} [inst : CommRing K] [inst_1 : CommRing L] [inst_2 : CommRing M]
(i : K →+* L) (j : K →+* M) (p : ℕ) [inst_3 : ExpChar M p] [inst_4 : ExpChar K p] [inst_5 : ExpChar L p]
[inst_6 : PerfectRing L p] [inst_7 : IsPerfectClosure i p] [inst_8 : PerfectRing M p] [inst_9 : IsPerfectClosure j p]
(x : L), (IsPerfectClosure.equiv j i p) ((IsPerfectClosure.equiv i j p) x) = x- Defined in
- Mathlib.FieldTheory.IsPerfectClosure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- RingEquivstatement · cited by 1,147
- ExpCharstatement and proof · cited by 276
- PerfectRingstatement and proof · cited by 154
- IsPerfectClosurestatement and proof · cited by 14
- IsPerfectClosure.equivstatement · cited by 13
- IsPerfectClosure.equiv_comp_equiv_applyproof · cited by 2
- IsPerfectClosure.equiv_self_applyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsPerfectClosure.equiv_comp_equiv_eq_idproof · cited by 0