Theorems · Theorem · order theory
WithBot.preimage_coe_Ioc
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, WithBot.some ⁻¹' Set.Ioc ↑b ↑a = Set.Ioc b a- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.preimagestatement and proof · cited by 4,946
- WithBotstatement · cited by 1,498
- Set.Ioiproof · cited by 1,463
- Set.Iicproof · cited by 1,111
- Set.Iocstatement · cited by 971
- WithBot.somestatement and proof · cited by 541
- WithBot.preimage_coe_Iicproof · cited by 5
- WithBot.preimage_coe_Ioiproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- WithBot.image_coe_Iocproof · cited by 2