Theorems · Theorem · order theory
LowerSet.sdiff_eq_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
- 2 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.
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 and proof · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Disjointstatement and proof · cited by 2,201
- LowerSetstatement and proof · cited by 230
- SetLike.coe_set_eqproof · cited by 27
- sdiff_eq_leftproof · cited by 15
- LowerSet.lowerproof · cited by 13
- LowerSet.sdiffstatement · cited by 8
- IsLowerSet.disjoint_upperClosure_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LowerSet.erase_eqproof · cited by 1
- LowerSet.sdiff_lt_leftproof · cited by 0