Theorems · Theorem · commutative algebra
AdicCompletion.mk_smul_top_ofAlgEquiv_symm
∀ {S : Type u_5} [inst : CommRing S] (I : Ideal S) [inst_1 : IsAdicComplete I S] (n : ℕ) (x : AdicCompletion I S),
(Ideal.Quotient.mk (I ^ n • ⊤)) ((AdicCompletion.ofAlgEquiv I).symm x) = (AdicCompletion.eval I S n) x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsAdicComplete
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- AlgEquivstatement · cited by 1,681
- AlgEquiv.symmstatement and proof · cited by 615
- Ideal.Quotient.mkstatement and proof · cited by 610
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.mk_ofAlgEquiv_symmproof · cited by 2