<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font><br/>  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b3">p2</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  holds <br/><font color="Olive" title="b1">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b2">p1</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Maroon" title="c2">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b2">p2</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  holds <br/><font color="Maroon" title="c2">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b1">p1</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  implies <font color="Maroon" title="c2">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">a</font> =  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">b</font> =  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:74"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font>
 <span class="kw">and </span><br/><a NAME="E2:74"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">f</font> =  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">g</font> =  <a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>);<br/>
<a NAME="E3:74"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="cat_3.html#T35" target="_self" title="CAT_3:th.35">Th39</a></span>;<br/>
<a NAME="E4:74"/><span class="kw">then </span>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>) &amp;  <a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T26" title="CAT_1:th.26">CAT_1:26</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">h</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E6:74"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<font color="Maroon" title="c2">c</font>)
 <span class="kw">and </span><br/><a NAME="E7:74"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<font color="Maroon" title="c2">c</font>) holds <br/>( ( <font color="Maroon" title="c3">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span> &amp; <font color="Maroon" title="c4">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>) ) iff <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D14" target="_self" title="CAT_3:def.14">Def16</a></span>;<br/>
<a NAME="E8:74"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E9:74"/><span class="lab"><font color="Green" title="E47">A6</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D14" target="_self" title="CAT_3:def.14">Def16</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">p</font> = <font color="Maroon" title="c3">p1</font> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T4" title="CAT_1:th.4">CAT_1:4</a></span>;<br/>
<a NAME="E11:74"/><span class="lab"><font color="Green" title="E48">A7</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>;<br/>
<a NAME="E12:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A8</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="cat_1.html#T17" title="CAT_1:th.17">CAT_1:17</a></span>;<br/>
<a NAME="E13:74"/><span class="lab"><font color="Green" title="E50">A9</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D14" target="_self" title="CAT_3:def.14">Def16</a></span>;<br/>
<a NAME="E14:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A10</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:74"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="cat_1.html#T17" title="CAT_1:th.17">CAT_1:17</a></span>;<br/>
<a NAME="E15:74"/><span class="lab"><font color="Green" title="E52">A11</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="cat_1.html#T17" title="CAT_1:th.17">CAT_1:17</a></span>;<br/>
<a NAME="E16:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A12</font></span>: 
<font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c2">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:74"><span class="lab"><font color="Green" title="E49">A8</font></span></a></span>;<br/>
<a NAME="E17:74"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:74"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="txt" href="#E15:74"><span class="lab"><font color="Green" title="E52">A11</font></span></a>, <a class="txt" href="#E12:74"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="cat_1.html#T17" title="CAT_1:th.17">CAT_1:17</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E54">A13</font></span>: <font color="Maroon" title="c4">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span> = 
 <a href="cat_3.html#K9" title="CAT_3:func.9">term</a> (<font color="Maroon" title="c2">c</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E14:74"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="ref" href="cat_3.html#T36" target="_self" title="CAT_3:th.36">Th40</a></span>
<br/>.= 
<font color="Maroon" title="c4">p2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E13:74"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="ref" href="cat_3.html#T36" target="_self" title="CAT_3:th.36">Th40</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E19:74"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c2">c</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="cat_1.html#T2" title="CAT_1:th.2">CAT_1:2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_1.html#D14" title="CAT_1:def.14">CAT_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font>, <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c3">p1</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c10">p</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">p</font> is  <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c9">h</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_1.html#D9" title="CAT_1:def.9">CAT_1:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font> &amp; <font color="Maroon" title="c10">p</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font></span>)</span> &amp; <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E20:74"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">p</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font></span>)</span> &amp; <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E21:74"/>
<font color="Maroon" title="c10">p</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E7:74"><span class="lab"><font color="Green" title="E45">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font></span>)</span></span><br/>

<span class="kw">then </span><font color="Maroon" title="c3">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c10">p</font></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E11:74"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></span>
<br/>.= 
<font color="Maroon" title="c10">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T21" title="CAT_1:th.21">CAT_1:21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E23:74"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E9:74"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E18:74"><span class="lab"><font color="Green" title="E54">A13</font></span></a>, <a class="txt" href="#E16:74"><span class="lab"><font color="Green" title="E53">A12</font></span></a>, <a class="ref" href="cat_3.html#T58" target="_self" title="CAT_3:th.58">Th63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
