diff --git a/checker/terms.py b/checker/terms.py
index 4257bef..cdab253 100644
--- a/checker/terms.py
+++ b/checker/terms.py
@@ -4,7 +4,7 @@
 """
 
 from __future__ import annotations
-from typing import Callable
+from typing import Callable, Generator
 
 import copy
 
@@ -24,6 +24,24 @@ USABLE_VAR_NAMES = [
     'μ', 'ν', 'ξ', 'ο', 'π', 'ρ', 'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω'
 ]
 
+def contains(haystack : Term, needle : Term) -> bool:
+    """
+        Determine whether a given small term value is contained in a bigger
+        term.
+
+        :param haystack: The term to search through.
+        :type haystack: Term
+        :param needle: The term to find.
+        :type needle: Term
+        :return: Whether the needle was found in the haystack.
+        :rtype: bool
+    """
+    for term in haystack.rec_iter():
+        if term == needle:
+            return True
+    else:
+        return False
+
 def normalize(term : Term) -> Term:
     """
         Create a normalization function. This function simplifies functions as
@@ -78,6 +96,21 @@ def std_norm_iter(term : Term) -> Term:
             return term
 _known_norms.append(std_norm_iter)
 
+def replace(term : Term, old : Term, new : Term) -> Term:
+    """
+        Find and replace occurrences of a sub-term in a given term.
+
+        :param term: The original term to update.
+        :type term: Term
+        :param old: The term to find and replace.
+        :type old: Term
+        :param new: The new term to replace the old one with.
+        :type new: Term
+        :return: The replaced term result.
+        :rtype: Term
+    """
+    return traverse_bottom_up(f=lambda t : new if t == old else t, term=term)
+
 def traverse(f : Callable[[Term], Term], term : Term) -> Term:
     """
         Traverse through the tree back-and-forth, aiming to run the given
@@ -96,7 +129,7 @@ def traverse(f : Callable[[Term], Term], term : Term) -> Term:
     a, b = Term(), term
 
     while a != b:
-        a, b = b, traverse_bottom_up(f=f, term=traverse_top_down(f=f, term=term))
+        a, b = b, traverse_bottom_up(f=f, term=traverse_top_down(f=f, term=b))
     
     return b
 
@@ -171,12 +204,6 @@ class Term:
         Base class for all terms.
     """
 
-    def __eq__(self, other) -> bool:
-        """
-            Determine whether two terms are equal.
-        """
-        return str(self) == str(other)
-
     def __repr__(self) -> str:
         """
             Create a representation of a term.
@@ -185,6 +212,12 @@ class Term:
     
     def normalize(self) -> Term:
         return normalize(term=self)
+    
+    def replace(self, old : Term, new : Term) -> Term:
+        return replace(term=self, old=old, new=new)
+    
+    def rec_iter(self) -> Generator[Term, None, None]:
+        yield self
 
     def to_str(self, vars : dict[str, Var]) -> str:
         return "<undefined>"
@@ -204,6 +237,11 @@ class App(Term):
             Create a representation of a term.
         """
         return self.to_str(vars={})
+    
+    def rec_iter(self) -> Generator[Term, None, None]:
+        yield self
+        yield from self.f.rec_iter()
+        yield from self.x.rec_iter()
 
     def to_str(self, vars: dict[str, Var]) -> str:
         f_str = self.f.to_str(vars=vars)
@@ -246,6 +284,18 @@ class Lambda(Term):
     out : Term
     var : Var
 
+    def __eq__(self, value: object) -> bool:
+        if not isinstance(value, Lambda):
+            return False
+        
+        for c in USABLE_VAR_NAMES:
+            if not contains(self.out, Const(c)):
+                return self.substitute(Const(c)) == value.substitute((Const(c)))
+        else:
+            raise ValueError(
+                "Ran out of usable variables for comparing lambda structures"
+            )
+
     def __init__(self, f : Callable[[Var], Term]) -> None:
         self.var = Var()
         self.out = f(self.var)
@@ -256,6 +306,10 @@ class Lambda(Term):
         """
         return self.to_str(vars={})
     
+    def rec_iter(self) -> Generator[Term, None, None]:
+        yield self
+        yield from self.out.rec_iter()
+    
     def replace_content(self, term : Term) -> Lambda:
         """
             Replace the content of the lambda function with the given term.
@@ -427,3 +481,15 @@ if __name__ == "__main__":
     g = L1(lambda b : A2(b, bool_f, bool_t))
     print(g)
     print(g.normalize())
+
+    print("\nFIND & REPLACE")
+    print(30 * "=")
+
+    h = A3(Const("f"), Const("x"), Const("y"), Const("z"))
+    i = A3(Const("f"), Const("x"), Const("b"), Const("z")).replace(
+        old=Const("b"), new=Const("y"),
+    )
+
+    print(h)
+    print(i)
+    assert h == i