Theorems · Theorem · functional analysis
ClosedSubmodule.toSubmodule_sInf
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : TopologicalSpace M]
[inst_3 : Module R M] (S : Set (ClosedSubmodule R M)), ↑(sInf S) = ⨅ s ∈ S, ↑s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- iInfstatement · cited by 1,690
- InfSet.sInfstatement · cited by 935
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.toSubmodule_iInfproof · cited by 1