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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">b1</font>, <font color="Maroon" title="c3">b2</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c3">b2</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c2">b1</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c3">b2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="txt" href="groeb_2.html#E1:13_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="polynom1.html#D13" title="POLYNOM1:def.13">POLYNOM1:def 13</a></i>;<br/><b>hence </b><a NAME="E2:13_1_1"/>
<font color="Maroon" title="c2">b1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">XXREAL_0:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:13_1"/>
 <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <font color="Maroon" title="c2">b1</font>,<font color="Maroon" title="c3">b2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">b1</font>
 <b>by </b><i><a class="ref" href="groeb_2.html#D2" target="_self" title="GROEB_2:def.2">Def2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:13"/>
( <font color="Maroon" title="c3">b2</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c2">b1</font> iff  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <font color="Maroon" title="c2">b1</font>,<font color="Maroon" title="c3">b2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">b1</font> )
 <b>by </b><i><a class="ref" href="groeb_2.html#T7" target="_self" title="GROEB_2:th.7">Th7</a></i>;<br/>


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