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18d. it's hard to hold mule close to donkey
?L?P?E?? If anser is slippery. Why?

Parsing for 10a. A medic provided treatment finally see = adrift

31a. Flawless runner managed to inspire one German . = unerring

1d. Withdraw notice about this in France and Germany = secede

Mule is a slipper + y ( end letter of donkey)

10a A DR (doctor) if (provided) + t last letter of treatment)

31 anagram of 'runner' + i (one) g (german)

1d notice : see
about
ce : French for this
+ d (Germany)

Very many thanks

You're welcome.
The last words of the clue 10a should be "at sea"