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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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17
lean/Spa/Lattice/IterProd.lean
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@@ -13,11 +13,6 @@ namespace IterProd
variable {A B : Type u}
instance lattice [Lattice A] [Lattice B] :
∀ k, Lattice (IterProd A B k)
| 0 => inferInstanceAs (Lattice B)
| k + 1 => @Prod.instLattice A (IterProd A B k) _ (lattice k)
instance decidableEq [DecidableEq A] [DecidableEq B] :
∀ k, DecidableEq (IterProd A B k)
| 0 => inferInstanceAs (DecidableEq B)
@@ -27,24 +22,14 @@ def build (a : A) (b : B) : (k : ℕ) → IterProd A B k
| 0 => b
| k + 1 => (a, build a b k)
variable [Lattice A] [Lattice B]
def fixedHeight [FiniteHeightLattice A] [FiniteHeightLattice B] :
∀ k, FiniteHeightLattice (IterProd A B k)
| 0 => inferInstanceAs (FiniteHeightLattice B)
| k + 1 => @Spa.prod A (IterProd A B k) _ (lattice k) _ (fixedHeight k)
| k + 1 => @Spa.prod A (IterProd A B k) _ (fixedHeight k)
instance finiteHeight [FiniteHeightLattice A] [FiniteHeightLattice B] (k : ℕ) :
FiniteHeightLattice (IterProd A B k) := fixedHeight k
lemma bot_fixedHeight [FiniteHeightLattice A] [FiniteHeightLattice B] :
∀ k, (fixedHeight (A := A) (B := B) k).bot = build (⊥ : A) (⊥ : B) k
| 0 => rfl
| k + 1 => by
show ((⊥ : A), (fixedHeight (A := A) (B := B) k).bot)
= ((⊥ : A), build (⊥ : A) (⊥ : B) k)
rw [bot_fixedHeight k]
end IterProd
end Spa