Theorems · Theorem · functional analysis
ClosedSubmodule.toSubmodule_sup
∀ {R : Type u_2} {N : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid N] [inst_2 : TopologicalSpace N]
[inst_3 : Module R N] [inst_4 : ContinuousAdd N] [inst_5 : ContinuousConstSMul R N] {s t : ClosedSubmodule R N},
↑(s ⊔ t) = ↑(↑s ⊔ ↑t).closure- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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 · cited by 7,192
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement · cited by 51
- Submodule.closurestatement · cited by 16
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