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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: NAT_6:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a> <br/>  for <font color="Olive" title="b3">n</font> being   <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a>  holds <br/> ( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b3">n</font> iff <font color="Olive" title="b1">x</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b3">n</font> )</div></div>
