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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2026-06-25 19:36:14 -05:00
parent cbad43efdc
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lean/Spa/Lattice/Unit.lean
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import Spa.Lattice
/-!
# Unit Lattice
This file provides a proof that in addition to being a lattice,
`PUnit` is a `Spa.FiniteHeightLattice`. This is fairly trivial result,
but the unit is used as a placeholder in various contexts (e.g.,
as a base case for the iterated product `Spa/Lattice/IterProd.lean`). -/
namespace Spa
/-- Since a singleton type's preorder has no nonempty `<` chains,
they are vacuously bounded by any minimum height. -/
lemma boundedChains_of_subsingleton (α : Type*) [Preorder α] [Subsingleton α]
(n : ℕ) : BoundedChains α n := fun c => by
by_contra hc