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\newenvironment{proof-of-lemma}[1]{\noindent{\bf Proof of Lemma #1: }\hspace*{1em}}{\qed\bigskip}
\newenvironment{proof-attempt}{\noindent{\bf Proof Attempt: }\hspace*{1em}}{\qed\bigskip}
\newenvironment{proofof}[1]{\noindent{\bf Proof: }
of #1:\hspace*{1em}}{\qed\bigskip}
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