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Theorems · Theorem · order theory

Interval.add_bot

∀ {α : Type u_2} [inst : Preorder α] [inst_1 : Add α] [inst_2 : AddLeftMono α] [inst_3 : AddRightMono α]
  (s : Interval α), s + ⊥ = ⊥
Defined in
Mathlib.Algebra.Order.Interval.Basic
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
PreorderAddAddLeftMonoAddRightMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Interval.length_add_le · cited by 2Interval.length_add_leInterval.add_eq_zero_iff · cited by 0Interval.add_eq_zero_iffInterval.bot_nsmul · cited by 0Interval.bot_nsmulPreorder · cited by 7952PreorderBot.bot · cited by 4720Bot.botAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoNonemptyInterval · cited by 139NonemptyIntervalInterval · cited by 76IntervalWithBot.map₂_bot_right · cited by 6WithBot.map₂_bot_rightInterval.add_botCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.