In the teaser for Rogue One we see some shots inside a hangar and in a control room (with Mon Mothma). It looks a lot like the hidden base from Episode IV.
Is this just an homage to the design, or is it meant to be the same base?
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Update 2. A screenshot directly from the film (complete with helpful subtitle).
Update: We now have proof-positive from the Mexican Rogue One publicity poster that the base in the film is indeed Yavin. This is also backed up by a tweet from the film's original screenwriter, Gary Whitta.
Whitta: Wow Mexico’s #RogueOne poster is heavy on the Yavin and appropriately gorgeous!
There's every indication that it's the same base, from the highly distinctive architecture, the equipment scattered about the base floor, the jerry-rigged drooping power conduits hanging from the ceiling and the low, oblong opening front door.
Mon Mothma's command chamber also seems to be identical (note the vine-covered stone walls behind the map screens)
Actually I realised of course they are... From Episode IV opening crawl
It is a period of civil war. Rebel spaceships, striking from a hidden base, have won their first victory against the evil Galactic Empire. During the battle, Rebel spies managed to steal secret plans to the Empire's ultimate weapon, the DEATH STAR
And from Episode V
It is a dark time for the Rebellion. Although the Death Star has been destroyed, Imperial troops have driven the Rebel forces from their hidden base and pursued them across the galaxy.
So I'm pretty sure canonically they are the same.