Theorems · Theorem · order theory

Set.disjoint_left_ordSeparatingSet

∀ {α : Type u_1} [inst : LinearOrder α] {s t : Set α}, Disjoint s (s.ordSeparatingSet t)

Defined in: Mathlib.Order.Interval.Set.OrdConnectedComponent
Cited by: 3 results in Mathlib
Foundations: Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder

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Cites12

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
LinearOrderstatement and proof · cited by 8,572
Compl.complproof · cited by 2,925
Set.iUnionproof · cited by 2,483
Disjointstatement · cited by 2,201
Disjoint.mono_rightproof · cited by 64
disjoint_compl_rightproof · cited by 47
Set.ordConnectedComponentproof · cited by 23
Set.ordSeparatingSetstatement · cited by 8
Set.disjoint_iUnion₂_rightproof · cited by 6
Disjoint.inter_right'proof · cited by 6
Set.ordConnectedComponent_subsetproof · cited by 3

Cited by3

Results whose statement or proof uses this declaration.

Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGEproof · cited by 2
Set.disjoint_right_ordSeparatingSetproof · cited by 1
Set.disjoint_ordT5Nhdproof · cited by 0