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Theorems · Theorem · order theory

BddAbove.add

∀ {M : Type u_3} [inst : Add M] [inst_1 : Preorder M] [AddLeftMono M] [AddRightMono M] {s t : Set M},
  BddAbove s → BddAbove t → BddAbove (s + t)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Bounds
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddPreorderAddLeftMonoAddRightMono
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Around this declaration

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

Set.BddAbove.add · cited by 0BddAbove.addSet · cited by 53352SetPreorder · cited by 7952PreorderAddLeftMono · cited by 687AddLeftMonoBddAbove · cited by 620BddAboveAddRightMono · cited by 367AddRightMonoSet.add · cited by 338Set.addSet.Nonempty.mono · cited by 88Nonempty.monoSet.Nonempty.add · cited by 3Nonempty.addsubset_upperBounds_add · cited by 2subset_upperBounds_addBddAbove.addCITED BYCITES

Cites9

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Cited by1

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