<?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="Red">::  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="b2">p1</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="b3">p2</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="Red">::  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="b1">p1</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="b2">p2</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="Red">::  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="c3">p1</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="c4">p2</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="E1:80"/><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="E2:80"/><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="c3">p1</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="Red">::  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="c4">p2</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="c4">p2</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="c4">p2</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>;<br/>
<a NAME="E3:80"/>
(  <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="c4">p2</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="c3">p1</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> &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="c4">p2</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="c3">p1</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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="cat_3.html#T39" target="_self" title="CAT_3:th.39">Th39</a></span>;<br/>
<a NAME="E4:80"/><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="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="c4">p2</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> &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="c4">p2</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> <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="c4">p2</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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T55" title="CAT_1:th.55">CAT_1:55</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="E6:80"/><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="c4">p2</font></span>)</span>,<font color="Maroon" title="c2">c</font>
 <span class="kw">and </span><br/><a NAME="E7:80"/><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="c4">p2</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_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="c4">p2</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; <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_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="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="#E1:80"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D16" target="_self" title="CAT_3:def.16">Def16</a></span>;<br/>
<a NAME="E8:80"/><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="c4">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:80"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></span>;<br/>
<a NAME="E9:80"/><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="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="#E1:80"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D16" target="_self" title="CAT_3:def.16">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="c4">p2</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="c4">p2</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T22" title="CAT_1:th.22">CAT_1:22</a></span>;<br/>
<a NAME="E11:80"/><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="#E6:80"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></span>;<br/>
<a NAME="E12:80"/><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="#E8:80"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<a NAME="E13:80"/><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="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="#E1:80"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_3.html#D16" target="_self" title="CAT_3:def.16">Def16</a></span>;<br/>
<a NAME="E14:80"/><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="c3">p1</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="c3">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:80"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<a NAME="E15:80"/><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="#E9:80"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E8:80"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<a NAME="E16:80"/><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="#E12:80"><span class="lab"><font color="Green" title="E49">A8</font></span></a></span>;<br/>
<a NAME="E17:80"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1</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="#E13:80"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="txt" href="#E15:80"><span class="lab"><font color="Green" title="E52">A11</font></span></a>, <a class="txt" href="#E12:80"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E54">A13</font></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> = 
 <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="c3">p1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E14:80"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="ref" href="cat_3.html#T40" target="_self" title="CAT_3:th.40">Th40</a></span>
<br/>.= 
<font color="Maroon" title="c3">p1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:80"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E13:80"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="ref" href="cat_3.html#T40" target="_self" title="CAT_3:th.40">Th40</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E19:80"/>
 <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="c4">p2</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="#E9:80"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="cat_1.html#T19" title="CAT_1:th.19">CAT_1:19</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="cat_1.html#D17" title="CAT_1:def.17">CAT_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c4">p2</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="Red">::  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="Red">:: according to </font></span><a class="ref" href="cat_1.html#D12" title="CAT_1:def.12">CAT_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E20:80"/>
(  <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="#E9:80"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E6:80"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E21:80"/>
<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="#E6:80"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E7:80"><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="Red">::  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="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> = 
<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="#E9:80"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E8:80"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E11:80"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</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#T46" title="CAT_1:th.46">CAT_1:46</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E23:80"/>
 <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="#E1:80"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E9:80"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E18:80"><span class="lab"><font color="Green" title="E54">A13</font></span></a>, <a class="txt" href="#E16:80"><span class="lab"><font color="Green" title="E53">A12</font></span></a>, <a class="ref" href="cat_3.html#T63" target="_self" title="CAT_3:th.63">Th63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
