Register cases rules on lattice carriers for aesop automation

Tag the finite lattice carrier types with `@[aesop safe cases]`
(`AboveBelow`, `Sign`) so aesop performs the dominant proof step in this
framework -- case-splitting a lattice element -- automatically. Combined
with the existing `@[simp]` operation lemmas, this collapses the recurring
"case-split then reduce" proofs to a bare `aesop`:

  * AboveBelow's six lattice axioms drop their explicit `rcases`
  * Sign/Constant `plus_mono₂`/`minus_mono₂` become `by aesop`
  * Constant `plus_valid`/`minus_valid` shrink to a 2-line `rcases <;> simp_all`
  * `not_mk_lt_mk` is reexpressed via `le_cases`

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

lean/Spa/Lattice/AboveBelow.lean

@@ -10,6 +10,8 @@ inductive AboveBelow (α : Type*) where
 
 namespace AboveBelow
 
+attribute [aesop safe cases] AboveBelow
+
 instance {α : Type*} [ToString α] : ToString (AboveBelow α) where
   toString
     | bot => "⊥"
@@ -49,22 +51,22 @@ instance : Min (AboveBelow α) where
     (mk x ⊓ mk y : AboveBelow α) = if x = y then mk x else bot := rfl
 
 protected lemma sup_comm (a b : AboveBelow α) : a ⊔ b = b ⊔ a := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
+  aesop
 
 protected lemma sup_assoc (a b c : AboveBelow α) : a ⊔ b ⊔ c = a ⊔ (b ⊔ c) := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;> aesop
+  aesop
 
 protected lemma inf_comm (a b : AboveBelow α) : a ⊓ b = b ⊓ a := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
+  aesop
 
 protected lemma inf_assoc (a b c : AboveBelow α) : a ⊓ b ⊓ c = a ⊓ (b ⊓ c) := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;> aesop
+  aesop
 
 protected lemma sup_inf_self (a b : AboveBelow α) : a ⊔ a ⊓ b = a := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
+  aesop
 
 protected lemma inf_sup_self (a b : AboveBelow α) : a ⊓ (a ⊔ b) = a := by
-  rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
+  aesop
 
 instance : Lattice (AboveBelow α) :=
   Lattice.mk' AboveBelow.sup_comm AboveBelow.sup_assoc
@@ -189,13 +191,7 @@ def rank : AboveBelow α → ℕ
 lemma not_mk_lt_mk (x y : α) : ¬(mk x : AboveBelow α) < mk y := by
   intro h
   obtain ⟨hle, hne⟩ := lt_iff_le_and_ne.mp h
-  have hsup := le_iff.mp hle
-  rw [mk_sup_mk] at hsup
-  by_cases hxy : x = y
-  · rw [if_pos hxy] at hsup
-    exact hne hsup
-  · rw [if_neg hxy] at hsup
-    exact absurd hsup (by simp)
+  rcases le_cases hle with h | h | h <;> simp_all
 
 lemma rank_strictMono : StrictMono (rank : AboveBelow α → ℕ) := by
   intro a b hab