Thomas will begin stage 14 in yellow, with a one minute 39 second lead over Froome, with Tom Dumoulin 11 seconds further back.
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After the 188-kilometre ride from Saint-Paul-Trois-Chateaux, Astana rider Fraile caught Belgian Jasper Stuyven near the top of the Cote de Croix Neuve, a 3-kilometre ascent at an average gradient of 10.2 percent, and did not look back as he crossed the line.
"I can only renew my appeals for calm, for common sense, with regards to the riders who make up the Tour de France".
Nibali, who claimed his sole yellow jersey in 2014, was transported to hospital with a suspected vertebra fracture after coming down hard around 4km from the summit of the legendary Tour climb.
Explaining the incident post-stage, Nibali said: "The road became narrower and there were no barriers". Having first scaled the mountain as a 15-year-old, the UAE Team Emirates leader was keenly aware of what lay ahead, but he managed his suffering as best he could to limit the damage.
Alaphilippe Stuyven and Thomas featured in an early breakaway that built a lead over the main pack of nearly 20 minutes in the 14th stage, although none of the 32 escapees were a threat in the general classification.
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"(Appealing for calm) is a step in the right direction but I think there are more measures that can be taken, for sure".
After three gruelling stages in the Alps, the peloton enjoyed the closest thing to a day off as is possible in the middle of a Grand Tour on the relatively flat 167km trek from Bourg d'Oisans to Valence, and Team Sky delivered both Geraint Thomas and Chris Froome safely over the line to ensure there was no change to the general classification.
"With all the TV motorbikes, they're accelerating out of the corners and I just lost the wheels on one of those corners, so I just rode at my own tempo", Martin told Cyclingnews.
Thomas and Froome each promised to help each other, but personal self-interests may bring out the worst case scenario for Team Sky. Romain Bardet of AG2R La Mondiale came in third, finishing a second after Dumoulin.
The young Colombian climber Egan Bernal (Sky) showed on Alpe d'Huez that he is probably a future tour victor when he put in a ferocious stint to lead Froome and Thomas up the mountain.
When Froome accelerated, I followed him, and I felt good, too, but then there was this slowing down, and I went down.