diff --git a/lean/Spa/Lattice.lean b/lean/Spa/Lattice.lean
index d5b9de3..d3d67d3 100644
--- a/lean/Spa/Lattice.lean
+++ b/lean/Spa/Lattice.lean
@@ -56,10 +56,6 @@ structure PointedLTSeries (α : Type*) (f t : α)(n : ℕ) [Preorder α] where
   last_series : series.last = t
   length_series : series.length = n
 
-theorem BoundedChains.no_longer {α : Type*} [Preorder α] {n : ℕ}
-    (h : BoundedChains α n) (c : LTSeries α) : c.length ≠ n + 1 :=
-  fun hc => absurd (h c) (by omega)
-
 class FiniteHeightLattice (α : Type*) [Lattice α] extends Bot α, Top α where
   height : ℕ
   longest_chain : PointedLTSeries α ⊥ ⊤ height
@@ -78,9 +74,9 @@ theorem bot_le [FiniteHeightLattice α] : ∀ (a : α), ⊥ ≤ a := by
     have hlt : ⊥ ⊓ a < lc.series.head := by
       rw [lc.head_series]
       exact lt_of_le_of_ne inf_le_left heq
-    exact FiniteHeightLattice.chains_bounded.no_longer
-      (lc.series.cons (⊥ ⊓ a) hlt)
-      (by simp [RelSeries.cons_length, lc.length_series])
+    have hbound := FiniteHeightLattice.chains_bounded (lc.series.cons (⊥ ⊓ a) hlt)
+    rw [RelSeries.cons_length, lc.length_series] at hbound
+    omega
 
 end FixedHeight