Theorems · Theorem · order theory
WithBot.range_coe
∀ {α : Type u_1} [inst : Preorder α], Set.range WithBot.some = Set.Ioi ⊥- Defined in
- Mathlib.Order.Interval.Set.WithBotTop
- Cited by
- 15 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.
Cites12
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
- Bot.botstatement · cited by 4,720
- Set.rangestatement · cited by 4,705
- Set.extproof · cited by 2,266
- WithBotstatement and proof · cited by 1,498
- Set.Ioistatement · cited by 1,463
- WithBot.somestatement and proof · cited by 541
- Set.mem_rangeproof · cited by 102
- Set.mem_Ioiproof · cited by 80
- WithBot.bot_lt_iff_ne_botproof · cited by 3
- WithBot.ne_bot_iff_existsproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- WithBot.preimage_coe_Ioi_botproof · cited by 3
- WithBot.image_coe_Icoproof · cited by 3
- WithBot.image_coe_Iioproof · cited by 3
- WithBot.image_coe_Iooproof · cited by 3
- WithBot.coe_covBy_coeproof · cited by 3
- WithBot.image_coe_Iccproof · cited by 2
- WithBot.image_coe_Iocproof · cited by 2
- WithBot.isEmbedding_coeproof · cited by 2
- WithBot.image_coe_Iciproof · cited by 1
- WithBot.image_coe_Iicproof · cited by 1
- WithBot.image_coe_Ioiproof · cited by 1
- WithBot.isOpenEmbedding_coeproof · cited by 1