Theorems · Theorem · order theory
isGLB_iUnion_iff_of_isLUB
Deprecated since 2026-06-04Use isGLB_iUnion_iff_of_isGLB instead.
∀ {α : Type u_1} [inst : Preorder α] {ι : Sort u_2} {s : ι → Set α} {u : ι → α},
(∀ (i : ι), IsGLB (s i) (u i)) → ∀ (c : α), IsGLB (Set.range u) c ↔ IsGLB (⋃ i, s i) c- Defined in
- Mathlib.Order.Bounds.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Preorderstatement and proof · cited by 7,952
- Set.rangestatement · cited by 4,705
- Set.iUnionstatement and proof · cited by 2,483
- Set.Iicproof · cited by 1,111
- Set.iInterproof · cited by 1,084
- IsGLBstatement and proof · cited by 213
- lowerBoundsproof · cited by 212
- IsGLB.lowerBounds_eqproof · cited by 11
- lowerBounds_singletonproof · cited by 7
- Set.range_eq_iUnionproof · cited by 4
- isGLB_congrproof · cited by 2
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