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If you've ever wondered how exactly your drink of choice arrived in your glass, or exactly what will happen to you once you empty it, Proof makes an unparalleled drinking companion.
Pointing at the empties for proof.
My empty plate was proof enough for me.
Hence (N_{p}(t cap N_{q}(t)) is empty and the proof is complete.
If J is empty, then the proof is similar to that when J is nonempty, which we omit.
So, if you feel compelled to include any of these terms, support those "empty" adjectives with proof -- preferably quantified -- that they were not empty at all.
His mother had to give him two sachets of Plumpy'Nut per day and every week when she returned to the health facility, she had to bring the empty packets as proof that the child had completed the week's treatment.
Most of the tunnels beneath Beijing are now empty, their gas-proof hatches paved over and their 10-inch-thick, radiation-proof steel doors locked shut.
The stark crib — no blankets, no suffocating toys, totally sids-proof — empty of Gabe as well.
(3.21) This implies that the index set J is just an empty set and the proof of Claim 1 is finished.
Sometimes we regarded Hollywood's notice as flattery, since being on TV made the Gates seem more real and substantial (fiction will do that); other times the fame seemed like the grimmest of jokes, weekly proof of the empty pretensions of the place.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com