Theorems · Theorem · commutative algebra
AdicCompletion.congr_symm_apply
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Type u_3} [inst_3 : AddCommGroup N] [inst_4 : Module R N] (f : M ≃ₗ[R] N) (x : AdicCompletion I N),
(AdicCompletion.congr I f).symm x = (AdicCompletion.map I ↑f.symm) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmstatement · cited by 1,461
- LinearEquiv.toLinearMapstatement · cited by 1,171
- AdicCompletionstatement and proof · cited by 160
- AdicCompletion.mapstatement · cited by 24
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