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Theorems · Theorem · order theory

subset_lowerBounds_add

∀ {M : Type u_3} [inst : Add M] [inst_1 : Preorder M] [AddLeftMono M] [AddRightMono M] (s t : Set M),
  lowerBounds s + lowerBounds t ⊆ lowerBounds (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.

BddBelow.add · cited by 0BddBelow.addSet · cited by 53352SetPreorder · cited by 7952PreorderAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoSet.add · cited by 338Set.addlowerBounds · cited by 212lowerBoundssubset_upperBounds_add · cited by 2subset_upperBounds_addsubset_lowerBounds_addCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.