Re-write the IterProd proofs to couple lattice and finite height lattice

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2024-03-01 21:02:56 -08:00
parent 29898e738b
commit ca90f6509c
3 changed files with 94 additions and 85 deletions
--- a/Lattice/Unit.agda
+++ b/Lattice/Unit.agda
@@ -107,10 +107,13 @@ private
    isLongest {tt} {tt} (step (tt⊔tt≈tt , tt̷≈tt) _ _) = ⊥-elim (tt̷≈tt refl)
    isLongest (done _) = z≤n

+fixedHeight : IsLattice.FixedHeight isLattice 0
+fixedHeight = (((tt , tt) , longestChain) , isLongest)
+
 isFiniteHeightLattice : IsFiniteHeightLattice ⊤ 0 _≈_ _⊔_ _⊓_
 isFiniteHeightLattice = record
    { isLattice = isLattice
-    ; fixedHeight = (((tt , tt) , longestChain) , isLongest)
+    ; fixedHeight = fixedHeight
    }

 finiteHeightLattice : FiniteHeightLattice ⊤