<keyword>is</keyword>
<keyword>equivalent</keyword>
<keyword>to</keyword>
+ <keyword>we</keyword>
+ <keyword>need</keyword>
+ <keyword>prove</keyword>
+ <keyword>or</keyword>
+ <keyword>equivalently</keyword>
+ <keyword>by</keyword>
+ <keyword>done</keyword>
+ <keyword>proved</keyword>
+ <keyword>have</keyword>
+ <keyword>such</keyword>
+ <keyword>the</keyword>
+ <keyword>thesis</keyword>
+ <keyword>becomes</keyword>
+ <keyword>conclude</keyword>
+ <keyword>obtain</keyword>
+ <keyword>proceed</keyword>
+ <keyword>induction</keyword>
+ <keyword>case</keyword>
+ <keyword>hypothesis</keyword>
+ <keyword>know</keyword>
<!-- commands -->
<keyword>alias</keyword>