Theorems · Theorem · order theory
bot_le
∀ {α : Type u} [inst : LE α] [inst_1 : OrderBot α] {a : α}, ⊥ ≤ a- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 306 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 6 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- OrderBot.bot_leproof · cited by 6
Cited by324
Results whose statement or proof uses this declaration.
- le_bot_iffproof · cited by 116
- GaloisConnection.l_botproof · cited by 63
- Filter.isCobounded_le_of_botproof · cited by 58
- bot_lt_iff_ne_botproof · cited by 57
- bot_uniqueproof · cited by 57
- Filter.isBounded_ge_of_botproof · cited by 55
- iSup_negproof · cited by 49
- bot_sup_eqproof · cited by 32
- sup_bot_eqproof · cited by 31
- Ideal.comap_map_of_surjectiveproof · cited by 30
- OrderIso.map_botproof · cited by 30
- ContDiff.continuousproof · cited by 23
Showing the 200 most cited of 324.