Coq Exercise Solutions Needed

I need complete solutions for Coq exercises based on the template provided by Saira. All definitions, fixpoints, lemmas, and tests must work in both "section prefix" and "ilist".

Requirements:
- Follow Saira's file strictly; do not change signatures of lemmas, definitions, etc.
- Replace "admitted." with correct solutions.
- Ensure everything is working properly in both sections as per the template.

Ideal Skills and Experience:
- Proficiency in Coq, especially with definitions, fixpoints, and lemma proofs.
- Experience with formal verification and functional programming concepts.
- Ability to adhere to strict requirements and deliver timely solutions.

Please provide a timeframe for completion.