Theorems · Theorem · convex and discrete geometry
PointedCone.ofSubmodule_iSup
∀ {R : Type u_1} {E : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
[inst_3 : AddCommMonoid E] [inst_4 : Module R E] (s : Set (Submodule R E)), ↑(⨆ S ∈ s, S) = ⨆ S ∈ s, ↑S- Defined in
- Mathlib.Geometry.Convex.Cone.Pointed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- 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
- PartialOrderstatement and proof · cited by 6,410
- iSupstatement and proof · cited by 2,415
- IsOrderedRingstatement and proof · cited by 777
- PointedConestatement and proof · cited by 151
- sSup_eq_iSupproof · cited by 42
- PointedCone.ofSubmodulestatement and proof · cited by 21
- iSup_imageproof · cited by 12
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