Theorems · Theorem · order theory
IsLUB.mono
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α} {a b : α}, IsLUB s a → IsLUB t b → s ⊆ t → a ≤ b- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Preorderstatement and proof · cited by 7,952
- IsLUBstatement and proof · cited by 280
- upperBounds_mono_setproof · cited by 13
- IsLeast.monoproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- sSup_le_sSupproof · cited by 24
- le_iff_atom_le_impproof · cited by 1
- IsOrderRightAdjoint.right_monoproof · cited by 0