polished the proofs and added a version of the weakening lemma that does not use the variable convention
polished the proofs and added a version of the weakening lemma that does not use the variable convention

MerelyAPseudonym/isabelle,MerelyAPseudonym/isabelle,MerelyAPseudonym/isabelle,MerelyAPseudonym/isabelle,MerelyAPseudonym/isabelle,MerelyAPseudonym/isabelle