Theorems · Theorem · order theory
WithBot.image_coe_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithBot.some '' Set.Ioi a = Set.Ioi ↑a- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 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
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- WithBotstatement and proof · cited by 1,498
- Set.Ioistatement and proof · cited by 1,463
- WithBot.somestatement and proof · cited by 541
- bot_leproof · cited by 306
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- Set.inter_eq_self_of_subset_leftproof · cited by 52
- Set.Ioi_subset_Ioiproof · cited by 28
- WithBot.range_coeproof · cited by 15
- WithBot.preimage_coe_Ioiproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- WithBot.Ioi_coeproof · cited by 0