Theorems · Theorem · order theory
union_upperBounds_subset_upperBounds_inter
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α}, upperBounds s ∪ upperBounds t ⊆ upperBounds (s ∩ t)- 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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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
- Preorderstatement and proof · cited by 7,952
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- upperBoundsstatement · cited by 263
- Set.union_subsetproof · cited by 71
- upperBounds_mono_setproof · cited by 13
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