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Theorems · Theorem · order theory

Interval.bot_add

∀ {α : Type u_2} [inst : Preorder α] [inst_1 : Add α] [inst_2 : AddLeftMono α] [inst_3 : AddRightMono α]
  (t : Interval α), ⊥ + t = ⊥
Defined in
Mathlib.Algebra.Order.Interval.Basic
Cited by
2 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_iffPreorder · cited by 7952PreorderBot.bot · cited by 4720Bot.botAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoNonemptyInterval · cited by 139NonemptyIntervalInterval · cited by 76IntervalWithBot.map₂_bot_left · cited by 4WithBot.map₂_bot_leftInterval.bot_addCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.