Theorems · Theorem · order theory
LowerSet.sdiff_lt_left
∀ {α : Type u_1} [inst : Preorder α] {s : LowerSet α} {t : Set α}, s.sdiff t < s ↔ ¬Disjoint (↑s) t- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites10
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 · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Disjointstatement · cited by 2,201
- Iff.notproof · cited by 489
- LowerSetstatement and proof · cited by 230
- LE.le.lt_iff_neproof · cited by 34
- LowerSet.sdiffstatement · cited by 8
- LowerSet.sdiff_eq_leftproof · cited by 2
- LowerSet.sdiff_le_leftproof · cited by 2
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