Theorems · Theorem · order theory
sSup_insert
∀ {α : Type u_1} [inst : CompleteLattice α] {a : α} {s : Set α}, sSup (insert a s) = a ⊔ sSup s- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- isLUB_sSupproof · cited by 21
- IsLUB.sSup_eqproof · cited by 17
- IsLUB.insertproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Set.sUnion_insertproof · cited by 11
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2
- sSup_le_sSup_of_subset_insert_botproof · cited by 1
- Submodule.restrictScalars_supproof · cited by 1