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<b>let </b><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> iff ( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font> implies <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:137_1"/><i><font color="Green" title="E78">A1</font></i>: 
<font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font> )</span><br/><b>thus </b><a NAME="E2:137_1"/>
<font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font> )</span><br/>

<b>assume </b><a NAME="E1:137_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font></span><br/>

<a NAME="E2:137_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T77" target="_self" title="COHSP_1:th.77">Th77</a></i>;<br/>
<b>hence </b><a NAME="E3:137_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:137_1"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="cohsp_1.html#T77" target="_self" title="COHSP_1:th.77">Th77</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>thus </b><a NAME="E3:137_1"/>
<font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">y1</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">y2</font> )</span><br/>

<b>assume </b><a NAME="E1:137_1_2"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">y1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">y2</font></span><br/>

<a NAME="E2:137_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T78" target="_self" title="COHSP_1:th.78">Th78</a></i>;<br/>
<b>hence </b><a NAME="E3:137_1_2"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">y2</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:137_1"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="cohsp_1.html#T78" target="_self" title="COHSP_1:th.78">Th78</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:137"/><i><font color="Green" title="E78">A2</font></i>: 
( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font></span><br/>

<b>let </b><font color="Maroon" title="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> )</span><br/>

<b>assume </b><a NAME="E3:137"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font></span><br/>

<a NAME="E4:137"/><b>then </b>
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; ( ( <font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x1</font> ) or ( <font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c5">a</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">y1</font> ) ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T76" target="_self" title="COHSP_1:th.76">Th76</a></i>;<br/>
<b>hence </b><a NAME="E5:137"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E2:137"><i><font color="Green" title="E78">A2</font></i></a>, <a class="ref" href="cohsp_1.html#T77" target="_self" title="COHSP_1:th.77">Th77</a>, <a class="ref" href="cohsp_1.html#T78" target="_self" title="COHSP_1:th.78">Th78</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
