Theorems · Theorem · order theory
lowerBounds_mono_mem
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} ⦃a b : α⦄, b ≤ a → a ∈ lowerBounds s → b ∈ lowerBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- lowerBoundsstatement and proof · cited by 212
- ge_transproof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- IsGLB.lowerBounds_eqproof · cited by 11
- BddBelow.unionproof · cited by 1
- lowerBounds_monoproof · cited by 0