Theorems · Theorem · commutative algebra
AdicCompletion.ofPowSMul_val_apply
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{a b c : ℕ} (h : c = b + a) {x : AdicCompletion I ↥(I ^ a • ⊤)},
↑((AdicCompletion.ofPowSMul I M a) x) c = (Submodule.powSMulQuotInclusion I M h ⊤) (↑x b)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 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.
Cites19
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 and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Subtype.propproof · cited by 505
- Submodule.subtypeproof · cited by 480
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.ofPowSMul_ofValEqZeroproof · cited by 1
- AdicCompletion.ofPowSMul_injectiveproof · cited by 0