Theorems · Theorem · order theory
WithTop.image_coe_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithTop.some '' Set.Ioi a = Set.Ioo ↑a ⊤- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 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.
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
- Top.topstatement and proof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- WithTopstatement and proof · cited by 3,754
- Set.Ioistatement and proof · cited by 1,463
- Set.Ioostatement and proof · cited by 1,214
- WithTop.somestatement and proof · cited by 1,128
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- WithTop.range_coeproof · cited by 19
- Set.Ioi_inter_Iioproof · cited by 16
- WithTop.preimage_coe_Ioiproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- EReal.image_coe_Ioiproof · cited by 2
- ENNReal.image_coe_Ioiproof · cited by 0