Theorems · Theorem · order theory
sSup_sdiff_singleton_bot
∀ {α : Type u_1} [inst : CompleteLattice α] (s : Set α), sSup (s \ {⊥}) = sSup s- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Bot.botstatement and proof · cited by 4,720
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- LE.le.antisymmproof · cited by 507
- Set.sdiff_subsetproof · cited by 156
- sSup_le_sSupproof · cited by 24
- Set.subset_insert_sdiff_singletonproof · cited by 3
- sSup_le_sSup_of_subset_insert_botproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.sUnion_sdiff_singleton_emptyproof · cited by 1
- sSup_diff_singleton_botproof · cited by 0