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<a NAME="E1:18_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1 or 1 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">n</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T26" title="ORDINAL1:th.26">ORDINAL1:26</a></i>;<br/>
<a NAME="E2:18_1_1"/>
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies ( <font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="arytm_3.html#K3" title="ARYTM_3:func.3">*^</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )
 
<b>by </b><i><a class="ref" href="ordinal2.html#T52" title="ORDINAL2:th.52">ORDINAL2:52</a>, <a class="ref" href="ordinal3.html#D7" title="ORDINAL3:def.7">ORDINAL3:def 7</a></i>;<br/>
<a NAME="E3:18_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> 1 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="arytm_3.html#E1:18_1_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="ordinal3.html#T17" title="ORDINAL3:th.17">ORDINAL3:17</a>, <a class="ref" href="ordinal3.html#T23" title="ORDINAL3:th.23">ORDINAL3:23</a>, <a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E4:18_1_1"/><b>then </b>
( <font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">n</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="ordinal2.html#K11" title="ORDINAL2:func.11">*^</a> <font color="Maroon" title="c2">n</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">m</font> )
 
<b>by </b><i><a class="ref" href="ordinal2.html#T56" title="ORDINAL2:th.56">ORDINAL2:56</a>, <a class="ref" href="ordinal3.html#T77" title="ORDINAL3:th.77">ORDINAL3:77</a></i>;<br/>
<a NAME="E5:18_1_1"/><b>then </b>
( <font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">m</font> &amp; <font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:18_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="ordinal3.html#K6" title="ORDINAL3:func.6">div^</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#T22" title="ORDINAL1:th.22">ORDINAL1:22</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a><br/>


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