Theorems · Theorem · general topology
Filter.disjoint_atBot_principal_Ioi
∀ {α : Type u_3} [inst : Preorder α] (x : α), Disjoint Filter.atBot (Filter.principal (Set.Ioi x))- Defined in
- Mathlib.Order.Filter.AtTopBot.Disjoint
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Disjointstatement · cited by 2,201
- le_rflproof · cited by 1,558
- Set.Ioistatement and proof · cited by 1,463
- Filter.principalstatement · cited by 740
- Filter.atBotstatement · cited by 512
- Filter.mem_principal_selfproof · cited by 37
- Filter.Iic_mem_atBotproof · cited by 15
- Filter.disjoint_of_disjoint_of_memproof · cited by 15
- Set.Iic_disjoint_Ioiproof · cited by 6
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