Theorems · Theorem · order theory
IsLUB.insert
∀ {γ : Type u_3} [inst : SemilatticeSup γ] (a : γ) {b : γ} {s : Set γ}, IsLUB s b → IsLUB (insert a s) (a ⊔ b)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
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
- SemilatticeSupstatement and proof · cited by 785
- IsLUBstatement and proof · cited by 280
- Set.insert_eqproof · cited by 47
- isLUB_singletonproof · cited by 10
- IsLUB.unionproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- isLUB_pairproof · cited by 5
- sSup_insertproof · cited by 4
- csSup_insertproof · cited by 0
- csSup_insert'proof · cited by 0