Tweak HOMEBREW_NO_AUTO_UPDATE handling.

This can just live in `brew.sh` and then it doesn’t need repeated in
all the other places.

Library/Homebrew/brew.sh

@@ -235,6 +235,9 @@ update-preinstall() {
   then
     brew update --preinstall
   fi
+
+  # If we've checked for updates, we don't need to check again.
+  export HOMEBREW_NO_AUTO_UPDATE="1"
 }
 
 if [[ -n "$HOMEBREW_BASH_COMMAND" ]]

Library/Homebrew/cmd/update.sh

@@ -359,8 +359,6 @@ EOS
 
   # only allow one instance of brew update
   lock update
-  # prevent recursive updates
-  export HOMEBREW_NO_AUTO_UPDATE="1"
 
   git_init_if_necessary
   # rename Taps directories

Library/Homebrew/dev-cmd/test-bot.rb

@@ -920,7 +920,6 @@ module Homebrew
     end
 
     ENV["HOMEBREW_DEVELOPER"] = "1"
-    ENV["HOMEBREW_NO_AUTO_UPDATE"] = "1"
     ENV["HOMEBREW_SANDBOX"] = "1"
     ENV["HOMEBREW_RUBY_MACHO"] = "1" if RUBY_TWO
     ENV["HOMEBREW_NO_EMOJI"] = "1"