Theorems · Theorem · functional analysis
ClosedSubmodule.toSubmodule_iInf
∀ {ι : Sort u_1} {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : TopologicalSpace M] [inst_3 : Module R M] (f : ι → ClosedSubmodule R M), ↑(⨅ i, f i) = ⨅ i, ↑(f i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 and proof · cited by 7,192
- Set.rangeproof · cited by 4,705
- iInfstatement and proof · cited by 1,690
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement and proof · cited by 51
- iInf_rangeproof · cited by 27
- ClosedSubmodule.toSubmodule_sInfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.coe_iInfproof · cited by 1