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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: MONOID_0:47</font></span><br/></a><div class="add">(  <a href="binop_2.html#K23" title="BINOP_2:func.23">addnat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K9" title="BINOP_2:func.9">addreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> &amp;  <a href="binop_2.html#K23" title="BINOP_2:func.23">addnat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K20" title="BINOP_2:func.20">addint</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> )</div></div>
