Theorems · Theorem · commutative algebra
AdicCompletion.ext
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{x y : AdicCompletion I M}, (∀ (n : ℕ), ↑x n = ↑y n) → x = y- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 92 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.
Cites12
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 · 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
- AdicCompletionstatement and proof · cited by 160
- AdicCompletion.transitionMapstatement · cited by 49
Cited by20
Results whose statement or proof uses this declaration.
- AdicCompletion.map_compproof · cited by 3
- AdicCompletion.map_idproof · cited by 2
- AdicCompletion.map_surjectiveproof · cited by 2
- AdicCompletion.of_injective_iffproof · cited by 2
- AdicCompletion.of_surjective_iffproof · cited by 2
- AdicCompletion.ext_evalₐproof · cited by 1
- AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
- AdicCompletion.map_zeroproof · cited by 1
- AdicCompletion.mk_surjectiveproof · cited by 1
- AdicCompletion.mk_zero_ofproof · cited by 1
- AdicCompletion.ofPowSMul_ofValEqZeroproof · cited by 1
- AdicCompletion.ofTensorProduct_naturalityproof · cited by 1