I thought he saw it happen?
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He had left for Castle Black the day before. This is why I asked earlier in the thread if he only realized what she had done when he found the toy deer lying in those ashes in the snow. I think what we were supposed to get from that is that he 1) assumed Stannis' daughter had died, but 2) had been unaware she was burned at the stake at the urging of Melisandre. Finding the deer-- especially WHERE he found it-- got him thinking, and he put it all together.