Theorems · Theorem · order theory
Set.OrdConnected.IicExtend
∀ {α : Type u_1} [inst : LinearOrder α] {b : α} {s : Set ↑(Set.Iic b)},
s.OrdConnected → {x | Set.IicExtend (fun x => x ∈ s) x}.OrdConnected- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
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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
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Set.Iccproof · cited by 1,702
- le_rflproof · cited by 1,558
- Set.Iicstatement and proof · cited by 1,111
- Set.OrdConnectedstatement and proof · cited by 161
- Set.OrdConnected.outproof · cited by 47
- Set.projIicproof · cited by 13
- min_le_minproof · cited by 11
- Set.IicExtendstatement and proof · cited by 9
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