HTTPS Redirect to append www

Hi, I'm a fairly new to iRules, so am requesting some assistance. We have a domain: cardiosmart.org. We have 2 LB VS objects (http and https). We have iRules for both objects. The behavior when people type: cardiosmart.org into their browser is correct, it redirects to https://www.cardiosmart.org. However, if folks type: https://cardiosmart.org the "www" does not get appended. We want the "www" to be appended regardless of of what folks type. Below are the iRules I have for both objects and I'm not entirely sure what it all means, but the site is working as needed, other than the www redirect for https to include www.

Do I only need to modify the iRule on the HTTPS object to append an "s" to the "http" in this part: equals "http://cardiosmart.org" }?

Appreciate any assistance you all can provide!

Diane

iRule Associated w/HTTP object:

when HTTP_REQUEST {
if { [string tolower [HTTP::uri]] contains "/Videos.aspx" } { 
   if {[active_members Cardiosmart_HTTP] > 0} { 
      pool Cardiosmart_HTTP
   } else {HTTP::redirect "http://maintenance.acc.org" 
      event disable all 
   } 
 }
 else { HTTP::respond 301 Location https://www.cardiosmart.org[HTTP::uri]
 }
}

iRule Associated w/HTTPS object:

when HTTP_REQUEST { 
   if { [string tolower [HTTP::host]] contains "healthandwellness.cardiosmart.org" } {
     HTTP::redirect "https://www.cardiosmart.org[HTTP::uri]" 
   }
   if { [string tolower [HTTP::host]] equals "http://cardiosmart.org" } {
     HTTP::redirect "https://www.cardiosmart.org" 
   }
}