jq: how to select object based on key value

Suppose we have the following data structure, and we want to select on the public IPv4 address only:

{
   "ip_addresses":[
      {
         "address":"145.40.82.9",
         "address_family":4,
         "cidr":31,
         "gateway":"145.40.82.8",
         "netmask":"255.255.255.254",
         "network":"145.40.82.8",
         "public":true
      },
      {
         "address":"2604:1380:45e1:c100::1",
         "address_family":6,
         "cidr":127,
         "gateway":"2604:1380:45e1:c100::",
         "netmask":"ffff:ffff:ffff:ffff:ffff:ffff:ffff:fffe",
         "network":"2604:1380:45e1:c100::",
         "public":true
      },
      {
         "address":"10.67.3.1",
         "address_family":4,
         "cidr":31,
         "gateway":"10.67.3.0",
         "netmask":"255.255.255.254",
         "network":"10.67.3.0",
         "public":false
      }
   ]
}

In the example above, the following jq command can be used:

'jq( [.ip_addresses[] | select(.address_family==4)] | .[] | select(.public) )'

The breakdown for the jq command is as follow:

[.ip_addresses[] | select(.address_family==4)]

... selects the array of ip_addresses and uses the first select statement to create an array of IPv4 addresses (the array is necessary in case there are more than one).

| .[] | select(.public)

... takes the object created in the previous step and passes it to another select statement, in this case where public==true