Theorems · Theorem · order theory
WithBot.image_coe_Ioc
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, WithBot.some '' Set.Ioc b a = Set.Ioc ↑b ↑a- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 2 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.
Cites14
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.Iocstatement and proof · cited by 971
- WithBot.somestatement and proof · cited by 541
- bot_leproof · cited by 306
- Set.Subset.transproof · cited by 218
- 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
- Set.Ioc_subset_Ioi_selfproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- WithBot.Ioc_coeproof · cited by 0
- EReal.image_coe_Iocproof · cited by 0