Q: Windows option not available at boot after creating/deleting new partition

I came across this forum while searching for a solution to a problem I'm having in which the option to boot into Windows is not presented while holding down the OPT key during boot. I originally posted in another thread because it was the top result Google brought up for this issue, but I was asked to repost, so here it is. If anyone can help walk me through how to fix this, I would really appreciate it.

Basically, I wanted to increase the size of my Windows 10 bootcamp partition so I could install a game without having to uninstall any others. So I went into Disk Utility and tried to increase the size of the bootcamp partition, but it wouldn't let me. It would let me create a new empty partition, though, so I thought I could work with that. I made a new 5 GB partition, but once I tried rebooting into Windows, it wouldn't work. I didn't get the option to select Windows at boot; it just lists Macintosh HD at the only option. So I went back to Disk Utility and deleted the new partition I had made, returning the OS X partition to its original size, but it's still not allowing me to boot into Windows.

Below is the Terminal output for the commands listed in the other threads. I'm using an early 2013 MacBook Pro (retina) running OS X 10.11.4. Windows 10 is installed on the bootcamp partition. If it means anything, Bootcamp still shows up in Disk Utility and in Finder. Just not at boot.

$ diskutil list

/dev/disk0 (internal, physical):

   #:                                   TYPE NAME                        SIZE               IDENTIFIER

   0:      GUID_partition_scheme                                   *500.3 GB     disk0

   1:                                     EFI EFI                               209.7 MB     disk0s1 

   2:                  Apple_CoreStorage Macintosh HD        388.4 GB     disk0s2

   3:                              Apple_Boot Recovery HD          650.1 MB     disk0s3

   4:                Microsoft Basic Data BOOTCAMP            111.0 GB     disk0s4

/dev/disk1 (internal, virtual):

   #:                                 TYPE NAME                          SIZE             IDENTIFIER

   0:                        Apple_HFS Macintosh HD            +388.1 GB     disk1

                                               Logical Volume on disk0s2

                                               BADA0F47-13F7-4920-ABB4-2ED458405A0F

                                               Unlocked Encrypted

$ diskutil cs list

CoreStorage logical volume groups (1 found)

|

+-- Logical Volume Group E5C14C1F-1E21-4D66-98AC-5AE7969E32E1

    =========================================================

    Name:         Macintosh HD

    Status:       Online

    Size:         388418744320 B (388.4 GB)

    Free Space:   6533120 B (6.5 MB)

    |

    +-< Physical Volume 7E003CB6-6606-4617-BB5D-2082F61E64D7

    |   ----------------------------------------------------

    |   Index:    0

    |   Disk:     disk0s2

    |   Status:   Online

    |   Size:     388418744320 B (388.4 GB)

    |

    +-> Logical Volume Family 822B8A7C-F4C8-4EBD-954A-45D43FFC4388

        ----------------------------------------------------------

        Encryption Type:         AES-XTS

        Encryption Status:       Unlocked

        Conversion Status:       Complete

        High Level Queries:      Fully Secure

        |                        Passphrase Required

        |                        Accepts New Users

        |                        Has Visible Users

        |                        Has Volume Key

        |

        +-> Logical Volume BADA0F47-13F7-4920-ABB4-2ED458405A0F

            ---------------------------------------------------

            Disk:                  disk1

            Status:                Online

            Size (Total):          388055695360 B (388.1 GB)

            Revertible:            Yes (unlock and decryption required)

            LV Name:               Macintosh HD

            Volume Name:           Macintosh HD

            Content Hint:          Apple_HFS

$ sudo gpt -vv -r show /dev/disk0

gpt show: /dev/disk0: mediasize=500277790720; sectorsize=512; blocks=977105060

gpt show: /dev/disk0: Suspicious MBR at sector 0

gpt show: /dev/disk0: Pri GPT at sector 1

gpt show: /dev/disk0: Sec GPT at sector 977105059

      start           size                  index        contents

          0             1                                      MBR

          1             1                                      Pri GPT header

          2            32                                     Pri GPT table

         34            6     

         40           409600               1            GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B

     409640       758630360         2            GPT part - 53746F72-6167-11AA-AA11-00306543ECAC

  759040000    1269760             3            GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC

  760309760    216795136         4            GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7

  977104896        131     

  977105027         32                               Sec GPT table

  977105059          1                                Sec GPT header

$ sudo fdisk /dev/disk0

Disk: /dev/disk0 geometry: 60821/255/63 [977105060 sectors]

Signature: 0xAA55

         Starting         Ending

#: id     cyl       hd    sec -   cyl      hd      sec  [              start -              size]

-----------------------------------------------------------------------------

1: EE    1023   254   63  -  1023   254    63   [                  1 -         409639]   <Unknown ID>

2: AC   1023   254   63  -  1023   254    63   [        409640 -   758630360]   <Unknown ID>

3: AB   1023   254   63  -  1023   254    63   [  759040000 -       1269760]   Darwin Boot

4: 0C   1023   254   63  -  1023   254    63   [  760309760 -   216795136]   Win95 FAT32L