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Theorems · Theorem · order theory

sSup_add

∀ {M : Type u_1} [inst : CompleteLattice M] [inst_1 : AddGroup M] [AddLeftMono M] [AddRightMono M] (s t : Set M),
  sSup (s + t) = sSup s + sSup t
Defined in
Mathlib.Algebra.Order.Group.Pointwise.CompleteLattice
Cited by
1 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLatticeAddGroupAddLeftMonoAddRightMono
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Around this declaration

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

sSup_sub · cited by 0sSup_subSet · cited by 53352SetAddGroup · cited by 4410AddGroupCompleteLattice · cited by 1048CompleteLatticeSupSet.sSup · cited by 954SupSet.sSupAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMonoSet.add · cited by 338Set.addOrderIso.to_galoisConnection · cited by 32OrderIso.to_galoisConnect…OrderIso.addLeft · cited by 18OrderIso.addLeftOrderIso.addRight · cited by 16OrderIso.addRightsSup_image2_eq_sSup_sSup · cited by 5sSup_image2_eq_sSup_sSupsSup_addCITED BYCITES

Cites11

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Cited by1

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