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Make FiniteHeightLattice extend Lattice and derive Top/Bot

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Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-25 18:42:28 -05:00
parent acef0f202b
commit cbad43efdc
11 changed files with 61 additions and 102 deletions
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14
lean/Spa/Lattice/AboveBelow.lean
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@@ -223,17 +223,11 @@ lemma boundedChains : BoundedChains (AboveBelow α) 2 := fun c => by
omega
instance [Inhabited α] : FiniteHeightLattice (AboveBelow α) where
bot := bot
top := top
height := 2
toLattice := inferInstance
longestChain :=
{ series :=
((RelSeries.singleton _ bot).snoc (mk default)
(by rw [RelSeries.last_singleton]; exact bot_lt_mk default)).snoc top
(by rw [RelSeries.last_snoc]; exact mk_lt_top default)
head_series := by simp
last_series := by simp
length_series := by simp [RelSeries.snoc, RelSeries.append] }
((RelSeries.singleton _ bot).snoc (mk default)
(by rw [RelSeries.last_singleton]; exact bot_lt_mk default)).snoc top
(by rw [RelSeries.last_snoc]; exact mk_lt_top default)
chains_bounded := boundedChains
end AboveBelow