Theorems · Theorem · order theory
WithBot.preimage_coe_Iio
∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithBot.some ⁻¹' Set.Iio ↑a = Set.Iio a- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- WithBotstatement · cited by 1,498
- Set.Iiostatement · cited by 1,166
- WithBot.somestatement · cited by 541
- WithBot.coe_lt_coeproof · cited by 55
Cited by6
Results whose statement or proof uses this declaration.
- EReal.preimage_coe_Iioproof · cited by 3
- EReal.preimage_coe_Iio_topproof · cited by 3
- WithBot.image_coe_Iioproof · cited by 3
- WithBot.preimage_coe_Iooproof · cited by 1
- WithBot.preimage_coe_Icoproof · cited by 1
- WithBot.preimage_coe_Ioo_botproof · cited by 0