Theorems · Theorem · order theory
IsGLB.union
∀ {γ : Type u_3} [inst : SemilatticeInf γ] {a b : γ} {s t : Set γ}, IsGLB s a → IsGLB t b → IsGLB (s ∪ t) (a ⊓ b)If a is the greatest lower bound of s and b is the greatest lower bound of t,
then a ⊓ b is the greatest lower bound of s ∪ t.
- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SemilatticeInfstatement and proof · cited by 634
- IsGLBstatement and proof · cited by 213
- lowerBoundsproof · cited by 212
- le_infproof · cited by 107
- inf_le_of_left_leproof · cited by 17
- inf_le_of_right_leproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- IsGLB.insertproof · cited by 3
- sInf_unionproof · cited by 1
- IsLeast.unionproof · cited by 1
- csInf_unionproof · cited by 0