Theorems · Theorem · commutative algebra
AdicCompletion.mk_apply_coe
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_4) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(f : AdicCompletion.AdicCauchySequence I M) (n : ℕ), ↑((AdicCompletion.mk I M) f) n = (I ^ n • ⊤).mkQ (↑f n)- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.mkQstatement · cited by 232
- AdicCompletionstatement · cited by 160
Cited by10
Results whose statement or proof uses this declaration.
- AdicCompletion.map_compproof · cited by 3
- AdicCompletion.map_idproof · cited by 2
- AdicCompletion.map_injectiveproof · cited by 1
- AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
- AdicCompletion.mk_surjectiveproof · cited by 1
- AdicCompletion.mk_zero_ofproof · cited by 1
- AdicCompletion.evalₐ_mkproof · cited by 1
- AdicCompletion.sumInv_comp_sumproof · cited by 0
- AdicCompletion.sum_comp_sumInvproof · cited by 0
- AdicCompletion.map_exactproof · cited by 0