Decision maker lied about reports

Hello there again,
As I've already stated, I have lost my long standing mobility (standard rate) after reporting changes showing that I actually now qualify for advanced rate.
Whilst getting my evidence together for a mandatory reconsideration ( once again I would like to thank you for the advice you have already given me on this BIS) I discovered that the DWP have actually lied about reports from my GP and hospital consultant.

In the section Entitled "How I made my decision" she said she looked at all of the information available to her including, and I quote, "the information provided in the report from your GP" and "the information provided by the letter from your hospital Dr"
I have written to both and both have said they have not been asked for or provided any evidence to the DWP about me. My pain management consultant, who is the only hospital profession for whom I gave them details, even went on to say

" I'm really surprised to hear her pip has been taken away given how limited she was when I saw her- she had significant disability from the pain in her back at the time. Very happy for her to use my letters in the appeal. I would strongly question what evidence they used to withdraw her pip"

I have this in email form printed out ready to send, along with another email from my GP surgery confirming that they also had no such request and haven't sent any report or about me.

I am planning to send these emails along with my appeal.
Do you think my pain management consultants comments will help me and will it help my appeal by pointing out that the decision maker appears to have lied? I don't want to cause any hostility towards myself but I really feel this is unacceptable. I'm quite shocked to be honest and feel that they should be answerable for doing this.
Again, I would really appreciate any thoughts and guidance on how I should move forward with this information.
Many thanks
Lells