<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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"> for <font color="Olive" title="b1">PA</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font> holds <br/> ( <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Olive" title="b1">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">PA</font> &amp; <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Olive" title="b1">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font> )</span><br/><b>let </b><font color="Maroon" title="c2">PA</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">PA</font> &amp; <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font> )</span><br/>



<b>thus </b><a NAME="E1:48"/>
<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">PA</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>proof </b></a><div class="add">

<a NAME="E1:48_1"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
 
<b>by </b><i><a class="ref" href="partit1.html#T27" target="_self" title="PARTIT1:th.27">Th27</a></i>;<br/>
<a NAME="E2:48_1"/><i><font color="Green" title="E32">A2</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T38" target="_self" title="PARTIT1:th.38">Th38</a></i>;<br/>
<a NAME="E3:48_1"/><i><font color="Green" title="E33">A3</font></i>: 
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></i>;<br/>
<a NAME="E4:48_1"/><i><font color="Green" title="E34">A4</font></i>: 
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
 
<b>by </b><i><a class="ref" href="partit1.html#T38" target="_self" title="PARTIT1:th.38">Th38</a></i>;<br/>
<a NAME="E5:48_1"/>
 <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T36" target="_self" title="PARTIT1:th.36">Th36</a></i>;<br/>
<a NAME="E6:48_1"/><b>then </b><i><font color="Green" title="E35">A5</font></i>: 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T24" target="_self" title="PARTIT1:th.24">Th24</a></i>;<br/>
<a NAME="E7:48_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:48_1_1"/>
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> holds <br/><font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">z</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="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> implies <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font> )</span><br/>

<b>assume </b><a NAME="E1:48_1_1_1"/><i><font color="Green" title="E36">A6</font></i>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:48_1_1_1_1_1"/>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font> or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font> )
 </span><b>by </b><i><a class="txt" href="partit1.html#E1:48_1_1_1"><i><font color="Green" title="E36">A6</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:48_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span><br/><div class="add"><b>hence </b><a NAME="E2:48_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 <b>by </b><i><a class="txt" href="partit1.html#E2:48_1"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="partit1.html#E6:48_1"><i><font color="Green" title="E35">A5</font></i></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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:48_1_1_1_1_1_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span><br/><div class="add"><b>hence </b><a NAME="E2:48_1_1_1_1_1_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 ; <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></div><b>end;</b></div>
<b>hence </b><a NAME="E3:48_1_1_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 ; <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>
<a NAME="E2:48_1_1"/><b>then </b><i><font color="Green" title="E36">A7</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:48_1_1"/>
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>hence </b><a NAME="E4:48_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font>
 <b>by </b><i><a class="txt" href="partit1.html#E2:48_1_1"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
<a NAME="E8:48_1"/><b>then </b><i><font color="Green" title="E36">A8</font></i>: 
<font color="Maroon" title="c2">PA</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="txt" href="partit1.html#E1:48_1"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="partit1.html#E3:48_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="partit1.html#E4:48_1"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="partit1.html#T24" target="_self" title="PARTIT1:th.24">Th24</a></i>;<br/>
<a NAME="E9:48_1"/>
 <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T36" target="_self" title="PARTIT1:th.36">Th36</a></i>;<br/>
<a NAME="E10:48_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font> <a href="partit1.html#NR1" title="PARTIT1:NR.1">'&lt;'</a> <font color="Maroon" title="c2">PA</font>
 
<b>by </b><i><a class="ref" href="partit1.html#T33" target="_self" title="PARTIT1:th.33">Th33</a></i>;<br/>
<b>hence </b><a NAME="E11:48_1"/>
<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K3" title="PARTIT1:func.3">'\/'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">PA</font>
 <b>by </b><i><a class="txt" href="partit1.html#E8:48_1"><i><font color="Green" title="E36">A8</font></i></a>, <a class="ref" href="partit1.html#T5" target="_self" title="PARTIT1:th.5">Th5</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="E2:48"/>
<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</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="48_2"><b>proof </b></a><div class="add">

 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c2">PA</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T28" target="_self" title="PARTIT1:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <font color="Maroon" title="c2">PA</font></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T38" target="_self" title="PARTIT1:th.38">Th38</a></i>
<br/>.= 
 <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <font color="Maroon" title="c1">Y</font>
<b>by </b><i><a class="ref" href="eqrel_1.html#T17" title="EQREL_1:th.17">EQREL_1:17</a></i>
<br/>.= 
 <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="partit1.html#T38" target="_self" title="PARTIT1:th.38">Th38</a></i>
;<br/>
<b>hence </b><a NAME="E2:48_2"/>
<span class="p1">(<span class="default"><a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c2">PA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partit1.html#NK6" title="PARTIT1:NK.6">%I</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="partit1.html#T29" target="_self" title="PARTIT1:th.29">Th29</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>
