The big giveaway if that the other sheep in the field are completely relaxed, to the extent they are also lying down.
even if something like a fox or a hare potters through a field with sheep in the sheep will stand and be 'on guard'. They sort of stand staring at the animal that's not supposed to be there.
The sheep in this field are apparently entirely unfazed by the alleged big cat munching on one of their mates.
and yes cows and sheep can share fields, if anyone was wondering (someone genuinely asked me that once).