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<b>let </b><font color="Maroon" title="c2">D1</font>, <font color="Maroon" title="c3">D2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13_1_2"/><i><font color="Green" title="E9">A2</font></i>: 
for <font color="Olive" title="b1">x1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D1</font> iff <font color="Olive" title="b1">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font> )
 <b>and </b><br/><a NAME="E2:13_1_2"/><i><font color="Green" title="E10">A3</font></i>: 
for <font color="Olive" title="b1">x1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D2</font> iff <font color="Olive" title="b1">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>thus </b><a NAME="E1:13_1_2_1"/>
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D1</font> implies <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_1"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D1</font>
 ;<br/>

<a NAME="E2:13_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c4">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="integra1.html#E1:13_1_2"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:13_1_2_1_1"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D2</font>
 <b>by </b><i><a class="txt" href="integra1.html#E2:13_1_2"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:13_1_2_1"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D2</font>
 ;<br/><a NAME="E3:13_1_2_1"/><b>then </b>
<font color="Maroon" title="c4">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="integra1.html#E2:13_1_2"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E4:13_1_2_1"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D1</font>
 <b>by </b><i><a class="txt" href="integra1.html#E1:13_1_2"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:13_1_2"/>
<font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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