How to create a new partition for OS X, then remove the original one
With Apple's OS X tools you can't expand the start sector of a partition to lower sector numbers. You have to choose another method.

You may accomplish your objective if less then one half of the net capacity of your hard drive ((~disk size - size of Recovery HD - size of EFI)/2) or less then one half of the main volume is occupied. If you miss the threshold narrowly you may remove swap files, sleepimage and clean the temp folders to lose further GBs.

In this particular case you may add a second volume with the same size as your then narrowed previous main volume, which is equivalent to splitting the available space in two equal volumes (with the first volume still containing your old OS X installation).

After installing your new OS X to the new volume ("El Capitan") you may transfer your apps, settings and data to the new volume.

After migrating your stuff you have to delete the old CoreStorage Logical Volume Group (the superior Macintosh HD) with:

diskutil cs delete lvgUUID


with lvgUUID: UUID of the Logical Volume Group. To get the lvgUUID use:

diskutil cs list


Deleting the Logical Volume Group will automatically create one new classical JHFS+ volume with the name "Untitled" occupying all available space on the disk. 

Now clone your new volume "El Capitan" to the empty volume "Untitled" with an appropriate tool (Disk Utility/Carbon Copy CLoner). The former "Untitled" will be renamed to "El Capitan". So rename the former "El Capitan" to "El Capitan_Old"

After successfully booting from "El Capitan", delete "El Capitan_Old" with Disk Utility and expand "El Capitan" to the full available size of your disk.



If more than one half of your (old) main volume is occupied you need an external disk to migrate or you have to delete some data.