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

<span class="kw">set </span><font color="Maroon" title="c3">C1</font> = <font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">C2</font> = <font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> = <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default">$1 <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default">$1 <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default">$1 <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span><span class="kw"> such that </span><br/><a NAME="E2:60_1_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
for <font color="Olive" title="b1">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> holds  <font color="Maroon" title="c5">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">m</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></span>
<a NAME="E3:60_1_1"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E4:60_1_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">F</font> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:60_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">F</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:60_1_1_1"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <span class="kw">and </span><br/><a NAME="E4:60_1_1_1"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">m</font> = <font color="Maroon" title="c7">m</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60_1_1_1"><span class="lab"><font color="Green" title="E40">A3</font></span></a></span>;<br/>
<a NAME="E6:60_1_1_1"/><span class="lab"><font color="Green" title="E42">A5</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:60_1_1_1"><span class="lab"><font color="Green" title="E41">A4</font></span></a></span>;<br/>
<a NAME="E7:60_1_1_1"/><span class="lab"><font color="Green" title="E43">A6</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="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </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> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>;<br/>
<a NAME="E8:60_1_1_1"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
<font color="Maroon" title="c8">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>;<br/>
<a NAME="E9:60_1_1_1"/><span class="lab"><font color="Green" title="E45">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="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span> <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="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T23" target="_self" title="CAT_5:th.23">Th23</a></span>;<br/>
<a NAME="E10:60_1_1_1"/><span class="lab"><font color="Green" title="E46">A9</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_5.html#K12" title="CAT_5:func.12">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="c2">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T27" target="_self" title="CAT_5:th.27">Th27</a></span>;<br/>
<a NAME="E11:60_1_1_1"/><span class="lab"><font color="Green" title="E47">A10</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_5.html#K12" title="CAT_5:func.12">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="c2">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T27" target="_self" title="CAT_5:th.27">Th27</a></span>;<br/>
<a NAME="E12:60_1_1_1"/><span class="lab"><font color="Green" title="E48">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="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </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> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60_1_1_1"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E9:60_1_1_1"><span class="lab"><font color="Green" title="E45">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="E13:60_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60_1_1_1"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E8:60_1_1_1"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="txt" href="#E9:60_1_1_1"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></span>;<br/>
<a NAME="E14:60_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">x</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1_1"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="#E10:60_1_1_1"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="txt" href="#E11:60_1_1_1"><span class="lab"><font color="Green" title="E47">A10</font></span></a>, <a class="txt" href="#E12:60_1_1_1"><span class="lab"><font color="Green" title="E48">A11</font></span></a>, <a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:60_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</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><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">F</font> = <font color="Maroon" title="c5">F</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60_1_1"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E40">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>; <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" title="b1">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> st <font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">d</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c8">g</font> = <font color="Maroon" title="c7">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">h</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c8">g</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">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="c2">f</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T27" target="_self" title="CAT_5:th.27">Th27</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">d</font> = <font color="Maroon" title="c9">h</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c11">d</font> = <font color="Maroon" title="c10">d</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="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c11">d</font></span><br/><a NAME="E4:60_1_1_2"/><span class="lab"><font color="Green" title="E41">A13</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c7">c</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E5:60_1_1_2"/><span class="lab"><font color="Green" title="E42">A14</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c11">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c11">d</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c9">h</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E6:60_1_1_2"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60_1_1_2"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E7:60_1_1_2"/><span class="lab"><font color="Green" title="E44">A16</font></span>: 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60_1_1_2"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E8:60_1_1_2"/><span class="lab"><font color="Green" title="E45">A17</font></span>: 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60_1_1_2"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E9:60_1_1_2"/><span class="lab"><font color="Green" title="E46">A18</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c8">g</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="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T23" target="_self" title="CAT_5:th.23">Th23</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c9">h</font>,<font color="Maroon" title="c9">h</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font></span>)</span> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E6:60_1_1_2"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E7:60_1_1_2"><span class="lab"><font color="Green" title="E44">A16</font></span></a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c11">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:60_1_1_2"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="#E8:60_1_1_2"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="txt" href="#E9:60_1_1_2"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</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><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E41">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">m</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</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="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <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#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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="c7">m</font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c8">g1</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span>, <font color="Maroon" title="c9">g2</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">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="c2">f</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T27" target="_self" title="CAT_5:th.27">Th27</a></span>;<br/><a NAME="E2:60_1_1_3"/><span class="lab"><font color="Green" title="E42">A20</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T23" target="_self" title="CAT_5:th.23">Th23</a></span>;<br/><a NAME="E3:60_1_1_3"/><span class="lab"><font color="Green" title="E43">A21</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T23" target="_self" title="CAT_5:th.23">Th23</a></span>;<br/><a NAME="E4:60_1_1_3"/>
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/><span class="kw">then </span> <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="mcart_1.html#K17" title="MCART_1:func.17">`11</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>
<br/>.= 
<font color="Maroon" title="c8">g1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>
;<br/><a NAME="E6:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A22</font></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#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c8">g1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">g1</font></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E7:60_1_1_3"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>;<br/><a NAME="E8:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A23</font></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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E9:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A24</font></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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E10:60_1_1_3"/><span class="lab"><font color="Green" title="E47">A25</font></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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:60_1_1_3"><span class="lab"><font color="Green" title="E45">A23</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E11:60_1_1_3"/>
<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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <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#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:60_1_1_3"><span class="lab"><font color="Green" title="E45">A23</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c8">g1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E9:60_1_1_3"><span class="lab"><font color="Green" title="E46">A24</font></span></a>, <a class="txt" href="#E10:60_1_1_3"><span class="lab"><font color="Green" title="E47">A25</font></span></a></span>
<br/>.= 
 <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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_3"><span class="lab"><font color="Green" title="E42">A20</font></span></a>, <a class="txt" href="#E6:60_1_1_3"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>
;<br/> <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="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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="c7">m</font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span></span><br/><a NAME="E13:60_1_1_3"/>
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/><span class="kw">then </span> <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">g1</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="mcart_1.html#K18" title="MCART_1:func.18">`12</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>
<br/>.= 
<font color="Maroon" title="c9">g2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>
;<br/><a NAME="E15:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A26</font></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c9">g2</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c9">g2</font></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E16:60_1_1_3"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T29" target="_self" title="CAT_5:th.29">Th29</a></span>;<br/><a NAME="E17:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A27</font></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="c7">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T30" target="_self" title="CAT_5:th.30">Th30</a></span>;<br/><a NAME="E18:60_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A28</font></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="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E19:60_1_1_3"/><span class="lab"><font color="Green" title="E51">A29</font></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="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:60_1_1_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E20:60_1_1_3"/>
<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="c7">m</font></span>)</span></span>)</span> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <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#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:60_1_1_3"><span class="lab"><font color="Green" title="E49">A27</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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="c7">m</font></span>)</span></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c9">g2</font>,<font color="Maroon" title="c9">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E18:60_1_1_3"><span class="lab"><font color="Green" title="E50">A28</font></span></a>, <a class="txt" href="#E19:60_1_1_3"><span class="lab"><font color="Green" title="E51">A29</font></span></a></span>
<br/>.= 
 <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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60_1_1_3"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E15:60_1_1_3"><span class="lab"><font color="Green" title="E48">A26</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>
;<br/> <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><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">f1</font>, <font color="Maroon" title="c8">f2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>; <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="c8">f2</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="c7">f1</font> implies <font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f1</font></span>)</span> )</span><br/><span class="kw">consider </span><font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c10">b1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>, <font color="Maroon" title="c11">g1</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="E2:60_1_1_4"/><span class="lab"><font color="Green" title="E42">A30</font></span>: 
<font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c11">g1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">and </span><br/><a NAME="E3:60_1_1_4"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c10">b1</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="c11">g1</font>
 <span class="kw">and </span><br/><a NAME="E4:60_1_1_4"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c11">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">a2</font>, <font color="Maroon" title="c13">b2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">Hom</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>, <font color="Maroon" title="c14">g2</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="E6:60_1_1_4"/><span class="lab"><font color="Green" title="E43">A31</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c12">a2</font>,<font color="Maroon" title="c13">b2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">and </span><br/><a NAME="E7:60_1_1_4"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c13">b2</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="c14">g2</font>
 <span class="kw">and </span><br/><a NAME="E8:60_1_1_4"/>
<font color="Maroon" title="c12">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c14">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><a NAME="E9:60_1_1_4"/><span class="lab"><font color="Green" title="E44">A32</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f2</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T2" target="_self" title="CAT_5:th.2">Th2</a></span>;<br/><a NAME="E10:60_1_1_4"/><span class="lab"><font color="Green" title="E45">A33</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f1</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T2" target="_self" title="CAT_5:th.2">Th2</a></span>;<br/><a NAME="E11:60_1_1_4"/><span class="lab"><font color="Green" title="E46">A34</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1_4"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="txt" href="#E9:60_1_1_4"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E12:60_1_1_4"/><span class="lab"><font color="Green" title="E47">A35</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_4"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E10:60_1_1_4"><span class="lab"><font color="Green" title="E45">A33</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">ha1</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c16">ha2</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c12">a2</font>, <font color="Maroon" title="c17">hb1</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c18">hb2</font> = <font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c13">b2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cat_5.html#K12" title="CAT_5:func.12">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="c2">f</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T27" target="_self" title="CAT_5:th.27">Th27</a></span>;<br/><a NAME="E14:60_1_1_4"/><span class="lab"><font color="Green" title="E48">A36</font></span>: 
<font color="Maroon" title="c7">f1</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_4"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E15:60_1_1_4"/><span class="lab"><font color="Green" title="E49">A37</font></span>: 
<font color="Maroon" title="c7">f1</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_4"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E16:60_1_1_4"/><span class="lab"><font color="Green" title="E50">A38</font></span>: 
<font color="Maroon" title="c7">f1</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_4"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E17:60_1_1_4"/><span class="lab"><font color="Green" title="E51">A39</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1_4"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E18:60_1_1_4"/><span class="lab"><font color="Green" title="E52">A40</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1_4"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E19:60_1_1_4"/><span class="lab"><font color="Green" title="E53">A41</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1_4"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E20:60_1_1_4"/><span class="lab"><font color="Green" title="E54">A42</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c15">ha1</font>,<font color="Maroon" title="c17">hb1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c11">g1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E14:60_1_1_4"><span class="lab"><font color="Green" title="E48">A36</font></span></a>, <a class="txt" href="#E15:60_1_1_4"><span class="lab"><font color="Green" title="E49">A37</font></span></a>, <a class="txt" href="#E16:60_1_1_4"><span class="lab"><font color="Green" title="E50">A38</font></span></a></span>;<br/><a NAME="E21:60_1_1_4"/><span class="lab"><font color="Green" title="E55">A43</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c16">ha2</font>,<font color="Maroon" title="c18">hb2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<font color="Maroon" title="c14">g2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E17:60_1_1_4"><span class="lab"><font color="Green" title="E51">A39</font></span></a>, <a class="txt" href="#E18:60_1_1_4"><span class="lab"><font color="Green" title="E52">A40</font></span></a>, <a class="txt" href="#E19:60_1_1_4"><span class="lab"><font color="Green" title="E53">A41</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E22:60_1_1_4"/><span class="lab"><font color="Green" title="E56">A44</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">f2</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="c7">f1</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="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f1</font></span>)</span></span><br/><a NAME="E23:60_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A45</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c13">b2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">g2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c11">g1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1_4"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E6:60_1_1_4"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="txt" href="#E11:60_1_1_4"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E12:60_1_1_4"><span class="lab"><font color="Green" title="E47">A35</font></span></a>, <a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><a NAME="E24:60_1_1_4"/><span class="lab"><font color="Green" title="E58">A46</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c15">ha1</font>,<font color="Maroon" title="c18">hb2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">g2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c11">g1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:60_1_1_4"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E12:60_1_1_4"><span class="lab"><font color="Green" title="E47">A35</font></span></a>, <a class="txt" href="#E20:60_1_1_4"><span class="lab"><font color="Green" title="E54">A42</font></span></a>, <a class="txt" href="#E21:60_1_1_4"><span class="lab"><font color="Green" title="E55">A43</font></span></a>, <a class="txt" href="#E22:60_1_1_4"><span class="lab"><font color="Green" title="E56">A44</font></span></a>, <a class="ref" href="cat_5.html#D11" target="_self" title="CAT_5:def.11">Def11</a></span>;<br/><a NAME="E25:60_1_1_4"/><span class="lab"><font color="Green" title="E59">A47</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60_1_1_4"><span class="lab"><font color="Green" title="E57">A45</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E26:60_1_1_4"/><span class="lab"><font color="Green" title="E60">A48</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60_1_1_4"><span class="lab"><font color="Green" title="E57">A45</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/><a NAME="E27:60_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">g2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c11">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60_1_1_4"><span class="lab"><font color="Green" title="E57">A45</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E28:60_1_1_4"/>
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E24:60_1_1_4"><span class="lab"><font color="Green" title="E58">A46</font></span></a>, <a class="txt" href="#E25:60_1_1_4"><span class="lab"><font color="Green" title="E59">A47</font></span></a>, <a class="txt" href="#E26:60_1_1_4"><span class="lab"><font color="Green" title="E60">A48</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">F</font> = <font color="Maroon" title="c6">F</font> as    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60_1_1"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="txt" href="#E7:60_1_1"><span class="lab"><font color="Green" title="E41">A19</font></span></a>, <a class="ref" href="cat_1.html#T96" title="CAT_1:th.96">CAT_1:96</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">F</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">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> holds  <font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span><br/>

<span class="kw">thus </span><a NAME="E10:60_1_1"/>
for <font color="Olive" title="b1">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="cat_5.html#K14" title="CAT_5:func.14">-SliceCat</a> <span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> holds  <font color="Maroon" title="c7">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a> </span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a> </span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_1_1"><span class="lab"><font color="Green" title="E38">A1</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"> verum</span><br/>


</div>
