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<b>let </b><font color="Maroon">POS</font> be   <a href="analmetr.html#NM1">OrtAfSp</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">POS</font></span>)</span>, <font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">POS</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:70"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> )
 ;<br/>

<b>set </b><font color="Maroon">X</font> =  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<b>set </b><font color="Maroon">Y</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> ;<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">POS</font></span>)</span> ;<br/><a NAME="E4:70_1_1"/>
 <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T10" target="_self">Th10</a>, </i>;<br/><a NAME="E5:70_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">x'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T8" target="_self">Th8</a>, <a class="txt" href="analmetr.html#E12"><i><font color="Green">Lemma54</font></i></a></i>;<br/><b>hence </b><a NAME="E6:70_1_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x1</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">POS</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> ;<br/><a NAME="E4:70_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">x'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T10" target="_self">Th10</a>, <a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/><a NAME="E5:70_1_2"/><b>then </b>
 <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T8" target="_self">Th8</a>, <a class="txt" href="analmetr.html#E12"><i><font color="Green">Lemma54</font></i></a></i>;<br/><b>hence </b><a NAME="E6:70_1_2"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:70_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> iff <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T9" target="_self">Th9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:70"/>
 <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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