diff --git a/Library/Homebrew/cask_dependent.rb b/Library/Homebrew/cask_dependent.rb
index cb9841fb8b..36c28c5e2c 100644
--- a/Library/Homebrew/cask_dependent.rb
+++ b/Library/Homebrew/cask_dependent.rb
@@ -1,8 +1,17 @@
 # typed: true
 # frozen_string_literal: true
 
+require "requirement"
+
 # An adapter for casks to provide dependency information in a formula-like interface.
 class CaskDependent
+  # Defines a dependency on another cask
+  class Requirement < ::Requirement
+    satisfy(build_env: false) do
+      Cask::CaskLoader.load(cask).installed?
+    end
+  end
+
   attr_reader :cask
 
   def initialize(cask)
@@ -33,11 +42,21 @@ class CaskDependent
       dsl_reqs = @cask.depends_on
 
       dsl_reqs.arch&.each do |arch|
-        requirements << ArchRequirement.new([:x86_64]) if arch[:bits] == 64
-        requirements << ArchRequirement.new([arch[:type]])
+        arch = if arch[:bits] == 64
+          if arch[:type] == :intel
+            :x86_64
+          else
+            :"#{arch[:type]}64"
+          end
+        elsif arch[:type] == :intel && arch[:bits] == 32
+          :i386
+        else
+          arch[:type]
+        end
+        requirements << ArchRequirement.new([arch])
       end
       dsl_reqs.cask.each do |cask_ref|
-        requirements << Requirement.new([{ cask: cask_ref }])
+        requirements << CaskDependent::Requirement.new([{ cask: cask_ref }])
       end
       requirements << dsl_reqs.macos if dsl_reqs.macos
 
diff --git a/Library/Homebrew/dependencies.rb b/Library/Homebrew/dependencies.rb
index b3a12d9bff..3b107e9999 100644
--- a/Library/Homebrew/dependencies.rb
+++ b/Library/Homebrew/dependencies.rb
@@ -2,7 +2,6 @@
 # frozen_string_literal: true
 
 require "delegate"
-require "cask_dependent"
 
 # A collection of dependencies.
 #