some propositions about the reg were false. I changed them and advanced a little, but still stuck
using ring solver to solve one of the big plug equalities
ring solver can
Cherry-picking of some general refactoring commits from master into
coinduction-loops, to make developments nicer from here on

Conflicts:
	agda/src/PiWare/ProofSamples.agda
Cherry-picking into coinduction-loops: after meeting, improved a little proof samples, probably register is incorrect

Conflicts:
	agda/src/PiWare/ProofSamples.agda