Should we use follow lemma or follow from lemma?
In mathematics, some theorems of real life are proved on some existing lemmas.
Which comes first (following
lemma (1), we prove… or
following
from lemma (1), we prove…
Follow from is the standard way to use follow in this sense.
From Oxford : (sense 2. = Latin ). 2)
Be a logical consequence of something
It thus follows from this equation that the value must be negative
So X follows from lemma(1) or From lemma(1), X follows.
Should I use we prove more?
If X is very long, and you must include it last, go for:
Following from lemma (1), we have… X.
By/From lemma
X,… Or if it
is a complicated one and you want to make clear what you are using the lemma on, by applying lemma
X to object Y we get/obtain…
