Theorems · Theorem · order theory
WithBot.preimage_coe_Ioo_bot
∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithBot.some ⁻¹' Set.Ioo ⊥ ↑a = Set.Iio a- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
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Cites11
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
- Bot.botstatement and proof · cited by 4,720
- WithBotstatement · cited by 1,498
- Set.Ioostatement · cited by 1,214
- Set.Iiostatement and proof · cited by 1,166
- WithBot.somestatement and proof · cited by 541
- Set.inter_univproof · cited by 198
- WithBot.preimage_coe_Iioproof · cited by 6
- WithBot.preimage_coe_Ioi_botproof · cited by 3
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