Theorems · Theorem · order theory
DedekindCut.image_left_subset_lowerBounds
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → ∀ (A : DedekindCut α), f '' A.left ⊆ lowerBounds (f '' A.right)- Defined in
- Mathlib.Order.Completion
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- Foundations
- Depth 7 from the axioms · uses no axioms
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- Monotonestatement and proof · cited by 1,397
- lowerBoundsstatement · cited by 212
- DedekindCutstatement and proof · cited by 27
- DedekindCut.leftstatement and proof · cited by 16
- DedekindCut.rightstatement and proof · cited by 12
- Concept.rel_extent_intentproof · cited by 5
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