A proxy supports only http. No http"s". Connect method not supported.
In other words, a client can only visit http port 80. Anything else is unsupported.
Can Tor be used in such an environment? How?
EDIT: This questions is not about DPI. It is about the requirement to set an upstream http proxy in Tor's torrc proxy settings.
If your proxy cannot do CONNECT, you lose. Sorry.
Most proxies actually do connect - else how would you visit gmail or anything else doing https - but they only do it for https on port 443.
If your proxy does connect, set the HTTPProxy and HTTPSProxy config options in your torrc -- that will make tor make all requests through that proxy using the http proxy command CONNECT.
See the manual page for more details.
Depending on how restrictive your proxy is, you may also want to set the FascistFirewall option. This will cause it to only do CONNECTs to port 443, which works in most places.
A pluggable transport that transports Tor connection in normal HTTP would also work. But that doesn't exist (sufficiently) yet[1][2].
At the moment, if you have to use a HTTP proxy server and that proxy server doesn't support the CONNECT method then you are out of luck. There are plans to build a pluggable transport which carries TLS over HTTP, but there are a number of challenges, including:
There is a outline of some of these topics in a design document but at the moment there is no complete implemenation. Contributions are welcome though!
That's one of the Pluggable Transports jobs to make encrypted traffic look like plain HTTP.
So an obfs2/3 bridge running on port 80 could help you out.
