Theorems · Theorem · order theory
IsLeast.union
∀ {γ : Type u_3} [inst : LinearOrder γ] {a b : γ} {s t : Set γ}, IsLeast s a → IsLeast t b → IsLeast (s ∪ t) (min a b)If a is the least element of s and b is the least element of t,
then min a b is the least element of s ∪ t.
- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- le_totalproof · cited by 294
- inf_of_le_leftproof · cited by 186
- inf_of_le_rightproof · cited by 128
- IsLeaststatement and proof · cited by 122
- IsLeast.isGLBproof · cited by 23
- IsGLB.unionproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsLeast.insertproof · cited by 2