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Explanation
•John Doe clicks on the link.  It takes him to the CarRental service. 
•The CarRental service doesn't know who John Doe is, so it constructs an AuthnRequest and HTTP redirects John Doe to the Airline service with the AuthnRequest encoded as a query string on the HTTP redirect URL.
•The Airline service constructs an authentication Response and sends it back to the CarRental service via encoding it within an HTML form. 
•Thus, now John Doe is knocking on the CarRental doors with authentication papers in hand.