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Theorems · Theorem · order theory

Set.nonempty_Iic

∀ {α : Type u_1} [inst : Preorder α] {a : α}, (Set.Iic a).Nonempty
Defined in
Mathlib.Order.Interval.Set.Basic
Cited by
3 results in Mathlib
Foundations
Depth 8 from the axioms · uses propext
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.Ideal.principal · cited by 12Ideal.principalLowerSet.Iic_ne_bot · cited by 2LowerSet.Iic_ne_botisConnected_Iic · cited by 1isConnected_Iicnot_bddBelow_Iic · cited by 0not_bddBelow_IicPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptySet.Iic · cited by 1111Set.IicSet.self_mem_Iic · cited by 26Set.self_mem_IicSet.nonempty_IicCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.