Theorems · Theorem · order theory
LowerSet.lowerClosure_sup_sdiff
∀ {α : Type u_1} [inst : Preorder α] {s : LowerSet α} {t : Set α},
t ⊆ ↑s → (∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) → lowerClosure t ⊔ s.sdiff t = s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites8
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
- SetLike.coestatement and proof · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- LowerSetstatement and proof · cited by 230
- sup_commproof · cited by 165
- lowerClosurestatement and proof · cited by 83
- LowerSet.sdiffstatement and proof · cited by 8
- LowerSet.sdiff_sup_lowerClosureproof · cited by 2
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