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Slightly tweak AboveBelow proofs

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Danila Fedorin
2026-06-29 08:16:55 -05:00
parent 47d54f5b4b
commit 2598df690c
1 changed files with 4 additions and 10 deletions
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14
lean/Spa/Lattice/AboveBelow.lean
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@@ -32,6 +32,7 @@ any inherent structure beyond "matching exactly".
namespace Spa
/-- The above-below lattice, with bottom element `bot` and top element `top`. -/
@[aesop safe cases]
inductive AboveBelow (α : Type*) where
| bot
| top
@@ -40,8 +41,6 @@ inductive AboveBelow (α : Type*) where
namespace AboveBelow
attribute [aesop safe cases] AboveBelow
instance {α : Type*} [ToString α] : ToString (AboveBelow α) where
toString
| bot => "⊥"
@@ -108,14 +107,9 @@ instance : OrderTop (AboveBelow α) where
top := top
le_top := le_top'
lemma bot_lt_mk (x : α) : (bot : AboveBelow α) < mk x :=
lt_of_le_of_ne (bot_le' _) (by simp)
lemma mk_lt_top (x : α) : (mk x : AboveBelow α) < top :=
lt_of_le_of_ne (le_top' _) (by simp)
lemma bot_lt_top : (bot : AboveBelow α) < top :=
lt_of_le_of_ne (bot_le' _) (by simp)
lemma bot_lt_mk (x : α) : (bot : AboveBelow α) < mk x := lt_of_le_of_ne (bot_le' _) (by simp)
lemma mk_lt_top (x : α) : (mk x : AboveBelow α) < top := lt_of_le_of_ne (le_top' _) (by simp)
lemma bot_lt_top : (bot : AboveBelow α) < top := lt_of_le_of_ne (bot_le' _) (by simp)
lemma le_cases {a b : AboveBelow α} (h : a ≤ b) :
a = bot ∨ b = top ∨ a = b := by