Proof clean-up.
Proof clean-up.

- Do not use induction/elim when not necessary: use destruct or
  destructive intro-pattern instead.
- Do not use heavy automation when lightweight automation is enough.
- Prefer shorter proofs when it does not hinder readability.
- Do not rely on automatically generated names.
- Use bullets.

SkySkimmer/coq,Lionel-Rieg/coq,ejgallego/coq,ppedrot/coq,Matafou/coq,gares/coq,william-lawvere/coq,william-lawvere/coq,Matafou/coq,ejgallego/coq,coq/coq,Zimmi48/coq,letouzey/coq-wip,maximedenes/coq,amintimany/coq,maximedenes/coq,silene/coq,JasonGross/coq,gares/coq,SkySkimmer/coq,Matafou/coq,coq/coq,letouzey/coq-wip,amintimany/coq,Lionel-Rieg/coq,maximedenes/coq,silene/coq,gares/coq,SkySkimmer/coq,letouzey/coq-wip,amintimany/coq,Ptival/coq,Lionel-Rieg/coq,coq/coq,ppedrot/coq,Zimmi48/coq,Ptival/coq,ppedrot/coq,JasonGross/coq,william-lawvere/coq,letouzey/coq-wip,JasonGross/coq,letouzey/coq-wip,coq/coq,maximedenes/coq,Ptival/coq,Zimmi48/coq,ejgallego/coq,SkySkimmer/coq,gares/coq,silene/coq,maximedenes/coq,ppedrot/coq,Zimmi48/coq,JasonGross/coq,gares/coq,ejgallego/coq,ppedrot/coq