Theorems · Theorem · order theory
lowerBounds_mono
∀ {α : Type u_1} [inst : Preorder α] ⦃s t : Set α⦄, s ⊆ t → ∀ ⦃a b : α⦄, b ≤ a → a ∈ lowerBounds t → b ∈ lowerBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
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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
- lowerBounds_mono_setproof · cited by 12
- lowerBounds_mono_memproof · cited by 3
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