diff --git a/ProvenZk/Hash.lean b/ProvenZk/Hash.lean
index be914d1..a6572b8 100644
--- a/ProvenZk/Hash.lean
+++ b/ProvenZk/Hash.lean
@@ -2,10 +2,10 @@ import ProvenZk.Ext.Vector
 
 def Hash (F: Type) (n: Nat) : Type := Vector F n -> F
 
-def perfect_hash {F n} (h: Hash F n): Prop := ∀{i1 i2}, h i1 = h i2 → i1 = i2
+def CollisionResistant {F n} (h: Hash F n): Prop := ∀{i1 i2}, h i1 = h i2 → i1 = i2
 
-@[simp] theorem simp_hash {h : Hash F n} [Fact (perfect_hash h)] {a b : Vector F n}: h a = h b ↔ a = b := by
-    have : perfect_hash h := (inferInstance : Fact (perfect_hash h)).elim
+@[simp] theorem CollisionResistant_def {h : Hash F n} [Fact (CollisionResistant h)] {a b : Vector F n}: h a = h b ↔ a = b := by
+    have : CollisionResistant h := (inferInstance : Fact (CollisionResistant h)).elim
     apply Iff.intro
-    { apply (inferInstance : Fact (perfect_hash h)).elim }
-    { tauto }
\ No newline at end of file
+    { apply (inferInstance : Fact (CollisionResistant h)).elim }
+    { tauto }
diff --git a/ProvenZk/Merkle.lean b/ProvenZk/Merkle.lean
index 884f7fd..3b73cd4 100644
--- a/ProvenZk/Merkle.lean
+++ b/ProvenZk/Merkle.lean
@@ -280,7 +280,7 @@ def recover {depth : Nat} {F: Type} (H : Hash F 2) (ix : Vector Dir depth) (proo
 
 theorem equal_recover_equal_tree {depth : Nat} {F: Type} (H : Hash F 2)
   (ix : Vector Dir depth) (proof : Vector F depth) (item₁ : F) (item₂ : F)
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   :
   (recover H ix proof item₁ = recover H ix proof item₂) ↔ (item₁ = item₂) := by
   apply Iff.intro
@@ -474,7 +474,7 @@ theorem proof_ceritfies_item
   {depth : Nat}
   {F: Type}
   {H: Hash F 2}
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   (ix : Vector Dir depth)
   (tree : MerkleTree F H depth)
   (proof : Vector F depth)
@@ -502,7 +502,7 @@ theorem proof_insert_invariant
   {depth : Nat}
   {F: Type}
   {H: Hash F 2}
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   (ix : Vector Dir depth)
   (tree : MerkleTree F H depth)
   (old new : F)
@@ -523,7 +523,7 @@ theorem proof_insert_invariant
       simp [*]
     }
 
-theorem recover_proof_reversible {H : Hash α 2} [Fact (perfect_hash H)] {Tree : MerkleTree α H d} {Proof : Vector α d}:
+theorem recover_proof_reversible {H : Hash α 2} [Fact (CollisionResistant H)] {Tree : MerkleTree α H d} {Proof : Vector α d}:
   recover H Index Proof Item = Tree.root →
   Tree.proof Index = Proof := by
   induction d with
@@ -537,7 +537,7 @@ theorem recover_proof_reversible {H : Hash α 2} [Fact (perfect_hash H)] {Tree :
     simp [root, recover, proof]
     intro h
     split at h <;> {
-      have : perfect_hash H := (inferInstance : Fact (perfect_hash H)).out
+      have : CollisionResistant H := (inferInstance : Fact (CollisionResistant H)).out
       have := this h
       rw [Vector.vector_eq_cons, Vector.vector_eq_cons] at this
       casesm* (_ ∧ _)
@@ -551,7 +551,7 @@ theorem recover_proof_reversible {H : Hash α 2} [Fact (perfect_hash H)] {Tree :
 theorem recover_equivalence
   {F depth}
   (H : Hash F 2)
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   (tree : MerkleTree F H depth)
   (Path : Vector Dir depth)
   (Proof : Vector F depth)
@@ -572,7 +572,7 @@ theorem recover_equivalence
     . apply recover_proof_reversible (Item := Item)
       assumption
 
-theorem eq_root_eq_tree {H} [ph: Fact (perfect_hash H)] {t₁ t₂ : MerkleTree α H d}:
+theorem eq_root_eq_tree {H} [ph: Fact (CollisionResistant H)] {t₁ t₂ : MerkleTree α H d}:
   t₁.root = t₂.root ↔ t₁ = t₂ := by
   induction d with
   | zero => cases t₁; cases t₂; tauto
@@ -594,7 +594,7 @@ theorem eq_root_eq_tree {H} [ph: Fact (perfect_hash H)] {t₁ t₂ : MerkleTree
 lemma proof_of_set_is_proof
   {F d}
   (H : Hash F 2)
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   (Tree : MerkleTree F H d)
   (ix : Vector Dir d)
   (item : F):
@@ -638,7 +638,7 @@ lemma proof_of_set_is_proof
 lemma proof_of_set_fin
   {F d}
   (H : Hash F 2)
-  [Fact (perfect_hash H)]
+  [Fact (CollisionResistant H)]
   (Tree : MerkleTree F H d)
   (ix : Fin (2^d))
   (item : F):