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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c3">D9</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font><br/> for <font color="Olive" title="b2">T9</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">D9</font> holds  <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">T9</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">T</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</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">T9</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">D9</font> holds  <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c4">T</font>,<font color="Olive" title="b1">T9</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">T9</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">D9</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"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c4">T</font>,<font color="Maroon" title="c5">T9</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/>









<span class="kw">reconsider </span><font color="Maroon" title="c6">S</font> = <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c4">T</font>,<font color="Maroon" title="c5">T9</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> 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 <font color="Maroon" title="c1">C</font>,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"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:78_1"/>
for <font color="Olive" title="b1">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b2">dd9</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> st <font color="Maroon" title="c6">S</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="Olive" title="b1">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="b2">dd9</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">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds <br/> ( <font color="Maroon" title="c6">S</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="Olive" title="b1">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">S</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="Olive" title="b1">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> ) ) &amp; ( for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">g</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="Olive" title="b1">f</font> holds <br/><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_1"><span class="kw">proof </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 <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">  ex <font color="Olive" title="b1">dd9</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> st <font color="Maroon" title="c6">S</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">dd9</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">d</font> = <span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c4">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">d9</font> = <span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c5">T9</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c10">dd9</font> = <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c4">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c5">T9</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">S</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="c10">dd9</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c6">S</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">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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></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="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><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"><span class="p4">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c4">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <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></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_1.html#T104" title="CAT_1:th.104">CAT_1:104</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><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"><span class="p4">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c4">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</font></span>)</span></span>)</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"><span class="p4">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c5">T9</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">c</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_1.html#T104" title="CAT_1:th.104">CAT_1:104</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c10">dd9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T41" target="_self" title="CAT_2:th.41">Th41</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">thus </span><a NAME="E2:78_1"/>
for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds <br/> ( <font color="Maroon" title="c6">S</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="Olive" title="b1">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">S</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="Olive" title="b1">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">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"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">g</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="Olive" title="b1">f</font> holds <br/><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">S</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">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">S</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">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> )</span><br/>

<a NAME="E1:78_1_2"/>
( <font color="Maroon" title="c4">T</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">f</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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">T9</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">f</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="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T98" title="CAT_1:th.98">CAT_1:98</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c6">S</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">f</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">(<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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span></span>)</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="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></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="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T41" target="_self" title="CAT_2:th.41">Th41</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"><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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T38" target="_self" title="CAT_2:th.38">Th38</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</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">S</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">f</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span></span><br/>

<a NAME="E3:78_1_2"/>
( <font color="Maroon" title="c4">T</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">f</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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">T9</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">f</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="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T98" title="CAT_1:th.98">CAT_1:98</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c6">S</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">f</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">(<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#K2" title="GRAPH_1:func.2">cod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span></span>)</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#K2" title="GRAPH_1:func.2">cod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></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="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T41" target="_self" title="CAT_2:th.41">Th41</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"><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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T38" target="_self" title="CAT_2:th.38">Th38</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</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><span class="kw">let </span><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</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">g</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">f</font> implies <font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E3:78_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c8">g</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">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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span><br/><a NAME="E4:78_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A2</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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></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="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>;<br/><a NAME="E5:78_1"/>
( <font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span> &amp; <font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</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="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</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="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</a></span>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</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="#E4:78_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="cat_2.html#T39" target="_self" title="CAT_2:th.39">Th39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">T9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</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="ref" href="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</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">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T79" title="FUNCT_3:th.79">FUNCT_3:79</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>
<span class="kw">hence </span><a NAME="E3:78"/>
<span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c4">T</font>,<font color="Maroon" title="c5">T9</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">D9</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T96" title="CAT_1:th.96">CAT_1:96</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>
