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

<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</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"> ( <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font> &amp; <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> is   <a href="index_1.html#NM10" title="INDEX_1:NM.10">coIndexing</a> of <font color="Maroon" title="c1">C</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">H</font> = <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">I</font> = <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span>;<br/>
<a NAME="E1:54"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K9" title="INDEX_1:func.9">`2</a>  <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E2:54"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a>  <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E25">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">a</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"> <span class="p1">(<span class="default"><span class="p2"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p3">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K9" title="INDEX_1:func.9">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p4">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p4">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p5">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p3">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K9" title="INDEX_1:func.9">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">a</font></span>)</span> = 
 <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
<br/>.= 
 <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p4">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p4">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p5">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Maroon" title="c5">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</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>
<a NAME="E4:54"/>
for <font color="Olive" title="b1">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><span class="p2"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p3">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K9" title="INDEX_1:func.9">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p4">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p4">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p5">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">m</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p4">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p4">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p5">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="index_1.html#E31"><span class="lab"><font color="Green" title="E21">Lm3</font></span></a></span>;<br/>
<a NAME="E5:54"/><span class="kw">then </span>
<span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K9" title="INDEX_1:func.9">`2</a>  is    <a href="index_1.html#M2" title="INDEX_1:mode.2">ManySortedFunctor</a> of <span class="p1">(<span class="default"><span class="p2"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p3">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><span class="p2"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p3">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D7" target="_self" title="INDEX_1:def.7">Def7</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">H</font> = <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> as    <a href="index_1.html#M3" title="INDEX_1:mode.3">Indexing</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D8" target="_self" title="INDEX_1:def.8">Def8</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">m1</font>, <font color="Maroon" title="c7">m2</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"> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m2</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="c6">m1</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c6">m1</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:54_2"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">m2</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="c6">m1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c6">m1</font></span>)</span></span><br/><a NAME="E2:54_2"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c6">m1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><a NAME="E3:54_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m2</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E4:54_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c6">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c6">m1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_2"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</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">hence </span><a NAME="E8:54"/>
<span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> is   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="index_1.html#T6" target="_self" title="INDEX_1:th.6">Th6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> is   <a href="index_1.html#NM10" title="INDEX_1:NM.10">coIndexing</a> of <font color="Maroon" title="c1">C</font></span><br/>

<a NAME="E9:54"/>
for <font color="Olive" title="b1">m</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Olive" title="b1">m</font> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">m</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <font color="Olive" title="b1">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="index_1.html#E32"><span class="lab"><font color="Green" title="E22">Lm4</font></span></a></span>;<br/>
<a NAME="E10:54"/><span class="kw">then </span>
<font color="Maroon" title="c5">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a>  is    <a href="index_1.html#M2" title="INDEX_1:mode.2">ManySortedFunctor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">H</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D7" target="_self" title="INDEX_1:def.7">Def7</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">H</font> = <font color="Maroon" title="c5">H</font> as    <a href="index_1.html#M3" title="INDEX_1:mode.3">Indexing</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D8" target="_self" title="INDEX_1:def.8">Def8</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">m1</font>, <font color="Maroon" title="c8">m2</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"> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">m2</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">m1</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c8">m2</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:54_3"/>
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">m2</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">m1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c8">m2</font></span>)</span></span><br/><a NAME="E2:54_3"/><span class="lab"><font color="Green" title="E26">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><a NAME="E3:54_3"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c8">m2</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E4:54_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">m2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c7">m1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">H</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c8">m2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_3"><span class="lab"><font color="Green" title="E26">A5</font></span></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</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">hence </span><a NAME="E13:54"/>
<span class="p1"><a href="index_1.html#K10" title="INDEX_1:func.10">[</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">D</font></span>)</span>,<span class="p2">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><a href="index_1.html#K10" title="INDEX_1:func.10">]</a></span> is   <a href="index_1.html#NM10" title="INDEX_1:NM.10">coIndexing</a> of <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="index_1.html#T7" target="_self" title="INDEX_1:th.7">Th7</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>
