Cheat sheet

Marking	Meaning	Explanation
\(\bullet\)	task	What is the exact problem to solve
(a)	assumption	Given fact. Naming could be done differently but still using parentheses, e.g. (a), (b), ... or (1), (2),..., or (assume1), (assume2), ...
[b]	observation	Not directly given fact, but following already known facts. Naming could be done differently but still using square brackets e.g. [a], [b], ... or [1], [2], ... or [obs1], [obs2], ...
\(\Vdash\)	proof	Derivation or proof starts here. It separates derivation from task, assumtions and observations. It can be left out if there are no assumptions or observations.
{...}	motivation	Every relation (equality, equivalence etc.) have to be justified. The motivation explaneds why the ralation between two terms is true.
\(\square\)	proven	Task is completed.

Basic structure of structured derivation

\(\bullet\)	Task(The actual task or assignment.)
(a)	assumption\(_{1}\) (assumption is given fact (which is true))
(b)	assumption\(_{2}\)
\(\vdots\)
[1]	{motivation or justification why abbreviation is true}
	observation\(_{1}\) (this new fact is followed by assumptions or previous observations)
[2]	{motivation or justification why abbreviation is true}
	observation\(_{2}\)
\(\Vdash\)	\(t_{0}\) (first term, begin of proof)
\(=\)	{motivation or justification for why \(t_{0}=t_{1}\) holds} (here could be references to assumptions or observations)
	\(t_{1}\)
\(=\)	{motivation or justification for why \(t_{1}=t_{2}\) holds }
	\(t_{2}\)
\(\vdots\)
	\(t_{n-1}\)
\(=\)	{motivation or justification for why \(t_{n-1}=t_{n}\) holds}
	\(t_{n}\) (last term, could be also solution to task)
\(\square\)	(end of proof)