diff --git a/Fixedpoint.agda b/Fixedpoint.agda
index 5e9f109..3f28c38 100644
--- a/Fixedpoint.agda
+++ b/Fixedpoint.agda
@@ -73,15 +73,15 @@ aᶠ≈faᶠ : aᶠ ≈ f aᶠ
 aᶠ≈faᶠ = proj₂ fix
 
 private
-    stepPreservesLess : ∀ (g hᶜ : ℕ) (a₁ a₂ a : A) (a≈fa : a ≈ f a) (a₂≼a : a₂ ≼ a)
+    stepPreservesLess : ∀ (g hᶜ : ℕ) (a₁ a₂ b : A) (b≈fb : b ≈ f b) (a₂≼a : a₂ ≼ b)
                      (c : ChainA.Chain a₁ a₂ hᶜ) (g+hᶜ≡h : g + hᶜ ≡ suc h)
                      (a₂≼fa₂ : a₂ ≼ f a₂) →
-                     proj₁ (doStep g hᶜ a₁ a₂ c g+hᶜ≡h a₂≼fa₂) ≼ a
+                     proj₁ (doStep g hᶜ a₁ a₂ c g+hᶜ≡h a₂≼fa₂) ≼ b
     stepPreservesLess 0 _ _ _ _ _ _ c g+hᶜ≡sh _ rewrite g+hᶜ≡sh = ⊥-elim (ChainA.Bounded-suc-n boundedᴬ c)
-    stepPreservesLess (suc g') hᶜ a₁ a₂ a a≈fa a₂≼a c g+hᶜ≡sh a₂≼fa₂ rewrite sym (+-suc g' hᶜ)
+    stepPreservesLess (suc g') hᶜ a₁ a₂ b b≈fb a₂≼b c g+hᶜ≡sh a₂≼fa₂ rewrite sym (+-suc g' hᶜ)
         with ≈-dec a₂ (f a₂)
-    ...   | yes _ = a₂≼a
-    ...   | no  _ = stepPreservesLess g' _ _ _ a a≈fa (≼-cong ≈-refl (≈-sym a≈fa) (Monotonicᶠ a₂≼a)) _ _ _
+    ...   | yes _ = a₂≼b
+    ...   | no  _ = stepPreservesLess g' _ _ _ b b≈fb (≼-cong ≈-refl (≈-sym b≈fb) (Monotonicᶠ a₂≼b)) _ _ _
 
 aᶠ≼ : ∀ (a : A) → a ≈ f a → aᶠ ≼ a
 aᶠ≼ a a≈fa = stepPreservesLess (suc h) 0 ⊥ᴬ ⊥ᴬ a a≈fa (⊥ᴬ≼ a) (ChainA.done ≈-refl) (+-comm (suc h) 0) (⊥ᴬ≼ (f ⊥ᴬ))