Theorems · Theorem · functional analysis
ClosedSubmodule.coe_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 71 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · 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
- SetLike.coestatement and proof · cited by 8,199
- iInfstatement · cited by 1,690
- Set.iInterproof · cited by 1,084
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmoduleproof · cited by 51
- Submodule.coe_iInfproof · cited by 16
- ClosedSubmodule.toSubmodule_iInfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.mem_iInfproof · cited by 0