Is $1+\mathrm{lg}i=\mathrm{lg}(i+i)$?

I've been studying Sedgewick's "Algorithms" book and in proof of one proposition he writes the following:

the property is preserved because

$1+\mathrm{lg}i=\mathrm{lg}(i+i)\le \mathrm{lg}(i+j)=\mathrm{lg}k$

I cannot wrap my brain around the first part of this inequation, namely $1+\mathrm{lg}i=\mathrm{lg}(i+i)$. Can anyone offer an explanation? Thanks in advance!

I've been studying Sedgewick's "Algorithms" book and in proof of one proposition he writes the following:

the property is preserved because

$1+\mathrm{lg}i=\mathrm{lg}(i+i)\le \mathrm{lg}(i+j)=\mathrm{lg}k$

I cannot wrap my brain around the first part of this inequation, namely $1+\mathrm{lg}i=\mathrm{lg}(i+i)$. Can anyone offer an explanation? Thanks in advance!