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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">h</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c3">h</font> )
 ;<br/>

<div><i><font color="Green" title="E16">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E2:16_1"/><b>then </b>
<font color="Maroon" title="c2">j</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_d.html#D2" target="_self" title="NAT_D:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:16_1"/>
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">j</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="ref" href="nat_d.html#T6" target="_self" title="NAT_D:th.6">Th6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/>
<font color="Maroon" title="c3">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><a NAME="E2:16_2"/><b>then </b><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">h</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">h</font></span>)</span>
 <b>by </b><i><a class="ref" href="int_1.html#T86" title="INT_1:th.86">INT_1:86</a></i>;<br/><a NAME="E3:16_2"/>
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c3">h</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">h</font></span>)</span>
 <b>by </b><i><a class="txt" href="nat_d.html#E1:16"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="nat_d.html#T9" target="_self" title="NAT_D:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E4:16_2"/>
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">j</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="nat_d.html#E1:16"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="nat_d.html#E2:16_2"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nat_d.html#T10" target="_self" title="NAT_D:th.10">Th10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">j</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="nat_d.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>


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