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If e p ≡ e q, then from (3.3) we obtain ( a − b ) ( 1 − e p ) = 0. Since a − b ≢ 0, we get e p ≡ 1 and hence finish our proof from (3.1).
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Hence finishing the proof of this statement.
Hence the proof is finished.
Hence we finish our proof.
Hence, we finish the proof.
Hence, we finish the proof of Theorem 1.
Defago was first in that section and Svindal was second, hence the close finish.
This smart behaviour of MR-polishing fluid is utilized to precisely control the finishing forces, hence final surface finish.
Hence his ruthless finish at TPC Louisiana, where he set a new record low score at the famous course.
However, in the second practice problem, the final task of writing a complete solution algorithm was left blank for the participant to finish; hence, 'leaving gaps in this manner provides learners with an opportunity to practise their declarative knowledge' (Anonymous 2000a).
Hence time to finish included cases where a lizard would move right through the channel, and cases in which it did not move all the way through but went back to the starting terrarium or stayed somewhere in the channel, until it arrived at the receiving terrarium.
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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