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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>  st  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Olive" title="b2">F2</font> holds <br/>for <font color="Olive" title="b3">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Olive" title="b1">F1</font>, <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Olive" title="b2">F2</font> holds <br/> ( <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> &amp;  ex <font color="Olive" title="b4">u</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font> st <font color="Olive" title="b3">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Olive" title="b4">u</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">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="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font> implies for <font color="Olive" title="b1">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font>, <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font> holds <br/> ( <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp;  ex <font color="Olive" title="b2">u</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> st <font color="Olive" title="b1">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Olive" title="b2">u</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:39"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</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">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font>, <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font> holds <br/> ( <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp;  ex <font color="Olive" title="b2">u</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> st <font color="Olive" title="b1">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Olive" title="b2">u</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">t</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font>, <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</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="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp;  ex <font color="Olive" title="b1">u</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> st <font color="Maroon" title="c6">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Olive" title="b1">u</font> )</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <span class="kw">means </span>for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,$2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E33">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">o</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> implies  ex <font color="Olive" title="b1">m</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">o</font>,<font color="Olive" title="b1">m</font>] ) )</span><br/><span class="kw">assume </span><a NAME="E1:39_1"/>
<font color="Maroon" title="c7">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</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">m</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">o</font>,<font color="Olive" title="b1">m</font>] )</span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">a9</font> = <font color="Maroon" title="c7">o</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c9">f1</font>, <font color="Maroon" title="c10">f2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c11">tau</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c9">f1</font>,<font color="Maroon" title="c10">f2</font><span class="kw"> such that </span><br/><a NAME="E4:39_1"/>
<font color="Maroon" title="c9">f1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c10">f2</font>
 <span class="kw">and </span><br/><a NAME="E5:39_1"/><span class="lab"><font color="Green" title="E34">A3</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="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f1</font>
 <span class="kw">and </span><br/><a NAME="E6:39_1"/><span class="lab"><font color="Green" title="E35">A4</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="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f2</font> &amp; <font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">f1</font>,<font color="Maroon" title="c10">f2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c11">tau</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T9" target="_self" title="ISOCAT_2:th.9">Th9</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">m</font> = <font color="Maroon" title="c11">tau</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><span class="kw">take </span><font color="Maroon" title="c13">m</font> = <font color="Maroon" title="c12">m</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="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c13">m</font>] )</span><br/><span class="kw">thus </span><a NAME="E8:39_1"/>
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</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">S<sub>1</sub></font>[<font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c13">m</font>]</span><br/><span class="kw">thus </span><a NAME="E9:39_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c13">m</font>]
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c14">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</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="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font> implies <font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<font color="Maroon" title="c13">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_1_1"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</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">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<font color="Maroon" title="c13">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<a NAME="E2:39_1_1"/>
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<a NAME="E3:39_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A6</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/>
<a NAME="E4:39_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:39_1"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E1:39_1_1"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:39_1_1"/>
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<font color="Maroon" title="c13">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39_1"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E1:39_1_1"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E3:39_1_1"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</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></div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c7">t9</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:39"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
for <font color="Olive" title="b1">o</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">o</font>,<font color="Maroon" title="c7">t9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S1" title="FUNCT_2:sch.1">FUNCT_2:sch 1</a>(<a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E33">A2</font></span></a>);<br/></span>
<a NAME="E5:39"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">u9</font> =  <a href="isocat_2.html#K1" title="ISOCAT_2:func.1">uncurry</a> <font color="Maroon" title="c7">t9</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<a NAME="E7:39"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E36">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">ab</font> be   <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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</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="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">ab</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">ab</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">ab</font></span>)</span></span><br/><span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c11">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E2:39_2"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<font color="Maroon" title="c9">ab</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:39"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></span>;<br/><a NAME="E3:39_2"/>
( <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font> &amp; <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></span>;<br/><a NAME="E4:39_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a></span>;<br/><a NAME="E5:39_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span>)</span>
 ;<br/><a NAME="E6:39_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D18" title="NATTRA_1:def.18">NATTRA_1:def 18</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">G1</font>, <font color="Maroon" title="c13">G2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c14">t99</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c12">G1</font>,<font color="Maroon" title="c13">G2</font><span class="kw"> such that </span><br/><a NAME="E8:39_2"/><span class="lab"><font color="Green" title="E38">A11</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">G1</font>,<font color="Maroon" title="c13">G2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c14">t99</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E9:39_2"/><span class="lab"><font color="Green" title="E39">A12</font></span>: 
<font color="Maroon" title="c12">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c13">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D15" title="NATTRA_1:def.15">NATTRA_1:def 15</a></span>;<br/><a NAME="E10:39_2"/><span class="lab"><font color="Green" title="E40">A13</font></span>: 
<font color="Maroon" title="c12">G1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c13">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39_2"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><a NAME="E11:39_2"/><span class="lab"><font color="Green" title="E41">A14</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">G1</font>,<font color="Maroon" title="c13">G2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="lab"><font color="Green" title="E42">A15</font></span>: <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></span>
<br/>.= 
<font color="Maroon" title="c12">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:39_2"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>
;<br/><a NAME="E13:39_2"/><span class="lab"><font color="Green" title="E43">A16</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39_2"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><span class="lab"><font color="Green" title="E44">A17</font></span>: <font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></span>
<br/>.= 
<font color="Maroon" title="c13">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:39_2"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>
;<br/><font color="Maroon" title="c8">u9</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T2" target="_self" title="ISOCAT_2:th.2">Th2</a></span>
<br/>.= 
<font color="Maroon" title="c14">t99</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>
<br/>.= 
<font color="Maroon" title="c14">t99</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:39_2"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
;<br/><span class="kw">hence </span><a NAME="E16:39_2"/>
<font color="Maroon" title="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">ab</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">ab</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">ab</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_2"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E12:39_2"><span class="lab"><font color="Green" title="E42">A15</font></span></a>, <a class="txt" href="#E14:39_2"><span class="lab"><font color="Green" title="E44">A17</font></span></a>, <a class="txt" href="#E13:39_2"><span class="lab"><font color="Green" title="E43">A16</font></span></a>, <a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</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="E9:39"/><span class="lab"><font color="Green" title="E37">A18</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">a</font> be   <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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:39_3"/>
not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39"><span class="lab"><font color="Green" title="E36">A9</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>
<a NAME="E10:39"/>
<font color="Maroon" title="c8">u9</font> is    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:39_4"/>
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="nattra_1.html#D3" title="NATTRA_1:def.3">NATTRA_1:def 3</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">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> holds  <font color="Maroon" title="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">a</font> be   <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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</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="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span><br/>

<a NAME="E2:39_4"/>
<font color="Maroon" title="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39"><span class="lab"><font color="Green" title="E36">A9</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39_4"/>
<font color="Maroon" title="c8">u9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</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="c9">u</font> = <font color="Maroon" title="c8">u9</font> as    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> ;<br/>
<div><span class="lab"><font color="Green" title="E38">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_5"><span class="kw">now </span></a><div class="add"><a NAME="E1:39_5"/>
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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">FF1</font> = <font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c11">FF2</font> = <font color="Maroon" title="c5">F2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/><span class="kw">let </span><font color="Maroon" title="c12">ab1</font>, <font color="Maroon" title="c13">ab2</font> be   <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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c12">ab1</font>,<font color="Maroon" title="c13">ab2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies for <font color="Olive" title="b1">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c12">ab1</font>,<font color="Maroon" title="c13">ab2</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</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="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E3:39_5"/><span class="lab"><font color="Green" title="E39">A20</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c12">ab1</font>,<font color="Maroon" title="c13">ab2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c12">ab1</font>,<font color="Maroon" title="c13">ab2</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</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="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span></span><br/><a NAME="E4:39_5"/><span class="lab"><font color="Green" title="E40">A21</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c14">a2</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c15">b2</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E6:39_5"/><span class="lab"><font color="Green" title="E41">A22</font></span>: 
<font color="Maroon" title="c13">ab2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c14">a2</font>,<font color="Maroon" title="c15">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:39"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></span>;<br/><a NAME="E7:39_5"/>
( <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> &amp; <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></span>;<br/><a NAME="E8:39_5"/><span class="kw">then </span>
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a></span>;<br/><a NAME="E9:39_5"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span>)</span>
 ;<br/><a NAME="E10:39_5"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D18" title="NATTRA_1:def.18">NATTRA_1:def 18</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">G2</font>, <font color="Maroon" title="c17">H2</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c18">t2</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c16">G2</font>,<font color="Maroon" title="c17">H2</font><span class="kw"> such that </span><br/><a NAME="E12:39_5"/><span class="lab"><font color="Green" title="E42">A23</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">G2</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c18">t2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E13:39_5"/><span class="lab"><font color="Green" title="E43">A24</font></span>: 
<font color="Maroon" title="c16">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c17">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D15" title="NATTRA_1:def.15">NATTRA_1:def 15</a></span>;<br/><a NAME="E14:39_5"/><span class="lab"><font color="Green" title="E44">A25</font></span>: 
( <font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c18">t2</font> &amp; <font color="Maroon" title="c16">G2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c17">H2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:39_5"><span class="lab"><font color="Green" title="E42">A23</font></span></a>, <a class="txt" href="#E13:39_5"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c19">a1</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c20">b1</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E16:39_5"/><span class="lab"><font color="Green" title="E45">A26</font></span>: 
<font color="Maroon" title="c12">ab1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:39"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></span>;<br/><a NAME="E17:39_5"/>
( <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> &amp; <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></span>;<br/><a NAME="E18:39_5"/><span class="kw">then </span>
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a></span>;<br/><a NAME="E19:39_5"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span>)</span>
 ;<br/><a NAME="E20:39_5"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D18" title="NATTRA_1:def.18">NATTRA_1:def 18</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c21">G1</font>, <font color="Maroon" title="c22">H1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c23">t1</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c22">H1</font><span class="kw"> such that </span><br/><a NAME="E22:39_5"/><span class="lab"><font color="Green" title="E46">A27</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c22">H1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c23">t1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E23:39_5"/><span class="lab"><font color="Green" title="E47">A28</font></span>: 
<font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c22">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D15" title="NATTRA_1:def.15">NATTRA_1:def 15</a></span>;<br/><a NAME="E24:39_5"/><span class="lab"><font color="Green" title="E48">A29</font></span>: 
( <font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c23">t1</font> &amp; <font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c22">H1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:39_5"><span class="lab"><font color="Green" title="E46">A27</font></span></a>, <a class="txt" href="#E23:39_5"><span class="lab"><font color="Green" title="E47">A28</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="lab"><font color="Green" title="E49">A30</font></span>: <font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font> = 
<font color="Maroon" title="c8">u9</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="txt" href="#E16:39_5"><span class="lab"><font color="Green" title="E45">A26</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c19">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">b1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T2" target="_self" title="ISOCAT_2:th.2">Th2</a></span>
<br/>.= 
<font color="Maroon" title="c23">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c20">b1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:39_5"><span class="lab"><font color="Green" title="E48">A29</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
;<br/><a NAME="E26:39_5"/><span class="lab"><font color="Green" title="E50">A31</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:39_5"><span class="lab"><font color="Green" title="E47">A28</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E27:39_5"/><span class="lab"><font color="Green" title="E51">A32</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><a NAME="E28:39_5"/><span class="lab"><font color="Green" title="E52">A33</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><a NAME="E29:39_5"/>
( <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> &amp; <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></span>;<br/><a NAME="E30:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A34</font></span>: 
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c22">H1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c23">t1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E22:39_5"><span class="lab"><font color="Green" title="E46">A27</font></span></a></span>;<br/><a NAME="E31:39_5"/><span class="lab"><font color="Green" title="E54">A35</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:39_5"><span class="lab"><font color="Green" title="E47">A28</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E32:39_5"/>
( <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> &amp; <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></span>;<br/><a NAME="E33:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A36</font></span>: 
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">G2</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c18">t2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E12:39_5"><span class="lab"><font color="Green" title="E42">A23</font></span></a></span>;<br/><a NAME="E34:39_5"/><span class="lab"><font color="Green" title="E56">A37</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E35:39_5"/><span class="lab"><font color="Green" title="E57">A38</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c24">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c12">ab1</font>,<font color="Maroon" title="c13">ab2</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="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">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">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span></span><br/><a NAME="E36:39_5"/>
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="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c26">h</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E38:39_5"/><span class="lab"><font color="Green" title="E58">A39</font></span>: 
<font color="Maroon" title="c24">f</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"><font color="Maroon" title="c25">g</font>,<font color="Maroon" title="c26">h</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="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">g</font> = <font color="Maroon" title="c25">g</font> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c14">a2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="txt" href="#E16:39_5"><span class="lab"><font color="Green" title="E45">A26</font></span></a>, <a class="txt" href="#E6:39_5"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="txt" href="#E38:39_5"><span class="lab"><font color="Green" title="E58">A39</font></span></a>, <a class="ref" href="isocat_2.html#T14" target="_self" title="ISOCAT_2:th.14">Th14</a></span>;<br/><a NAME="E40:39_5"/><span class="lab"><font color="Green" title="E59">A40</font></span>: 
 <a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c27">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">FF2</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c27">g</font>
 ;<br/><a NAME="E41:39_5"/><span class="lab"><font color="Green" title="E60">A41</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c14">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="txt" href="#E16:39_5"><span class="lab"><font color="Green" title="E45">A26</font></span></a>, <a class="txt" href="#E6:39_5"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th13</a></span>;<br/><a NAME="E42:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A42</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c27">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c27">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">h</font> = <font color="Maroon" title="c26">h</font> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">b2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="txt" href="#E16:39_5"><span class="lab"><font color="Green" title="E45">A26</font></span></a>, <a class="txt" href="#E6:39_5"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="txt" href="#E38:39_5"><span class="lab"><font color="Green" title="E58">A39</font></span></a>, <a class="ref" href="isocat_2.html#T14" target="_self" title="ISOCAT_2:th.14">Th14</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">g9</font> = <font color="Maroon" title="c27">g</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">h9</font> = <font color="Maroon" title="c28">h</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">f9</font> = <font color="Maroon" title="c24">f</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> ;<br/><a NAME="E47:39_5"/><span class="lab"><font color="Green" title="E62">A43</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></span>;<br/><a NAME="E48:39_5"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A44</font></span>: <font color="Maroon" title="c29">g9</font> <a href="cat_1.html#K1" title="CAT_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="c19">a1</font></span>)</span> = 
<font color="Maroon" title="c27">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c27">g</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="cat_1.html#T58" title="CAT_1:th.58">CAT_1:58</a></span>
;<br/><a NAME="E50:39_5"/><span class="lab"><font color="Green" title="E64">A45</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c27">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></span>;<br/><a NAME="E51:39_5"/><span class="lab"><font color="Green" title="E65">A46</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c32">e1</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c27">g</font>, <font color="Maroon" title="c33">e2</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c27">g</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font></span>)</span> ;<br/><a NAME="E53:39_5"/><span class="lab"><font color="Green" title="E66">A47</font></span>: 
 <a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c27">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c10">FF1</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c27">g</font>
 ;<br/><a NAME="E54:39_5"/><span class="lab"><font color="Green" title="E67">A48</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><a NAME="E55:39_5"/><span class="lab"><font color="Green" title="E68">A49</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="txt" href="#E16:39_5"><span class="lab"><font color="Green" title="E45">A26</font></span></a>, <a class="txt" href="#E6:39_5"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th13</a></span>;<br/><a NAME="E56:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A50</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><a NAME="E57:39_5"/><span class="lab"><font color="Green" title="E70">A51</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c22">H1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:39_5"><span class="lab"><font color="Green" title="E46">A27</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E58:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A52</font></span>: 
<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c22">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A53</font></span>: <font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T47" title="CAT_2:th.47">CAT_2:47</a></span>
;<br/><a NAME="E60:39_5"/><span class="lab"><font color="Green" title="E73">A54</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">G2</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:39_5"><span class="lab"><font color="Green" title="E42">A23</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E61:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A55</font></span>: 
<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c17">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E62:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A56</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c17">H2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:39_5"><span class="lab"><font color="Green" title="E71">A52</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#T18" target="_self" title="ISOCAT_2:th.18">Th18</a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E63:39_5"/><span class="lab"><font color="Green" title="E76">A57</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c14">a2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c16">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:39_5"><span class="lab"><font color="Green" title="E73">A54</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c34">v1</font> = <font color="Maroon" title="c4">F1</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Maroon" title="c27">g</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c16">G2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:39_5"><span class="lab"><font color="Green" title="E70">A51</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E65:39_5"/><span class="lab"><font color="Green" title="E77">A58</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><a NAME="E66:39_5"/>
(  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c28">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a>, <a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A59</font></span>:  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</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"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<font color="Maroon" title="c28">h</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">b2</font></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#T38" title="CAT_2:th.38">CAT_2:38</a></span>
<br/>.= 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c27">g</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</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="#E50:39_5"><span class="lab"><font color="Green" title="E64">A45</font></span></a>, <a class="txt" href="#E47:39_5"><span class="lab"><font color="Green" title="E62">A43</font></span></a>, <a class="ref" href="cat_2.html#T38" title="CAT_2:th.38">CAT_2:38</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c35">v2</font> = <font color="Maroon" title="c5">F2</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Maroon" title="c27">g</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c22">H1</font>,<font color="Maroon" title="c17">H2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:39_5"><span class="lab"><font color="Green" title="E70">A51</font></span></a>, <a class="txt" href="#E61:39_5"><span class="lab"><font color="Green" title="E74">A55</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E69:39_5"/><span class="lab"><font color="Green" title="E79">A60</font></span>: 
<span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c29">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c22">H1</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c35">v2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:39_5"><span class="lab"><font color="Green" title="E71">A52</font></span></a>, <a class="txt" href="#E61:39_5"><span class="lab"><font color="Green" title="E74">A55</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#D4" target="_self" title="ISOCAT_2:def.4">Def4</a></span>;<br/><a NAME="E70:39_5"/><span class="lab"><font color="Green" title="E80">A61</font></span>: 
<font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c17">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:39_5"><span class="lab"><font color="Green" title="E71">A52</font></span></a>, <a class="txt" href="#E61:39_5"><span class="lab"><font color="Green" title="E74">A55</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#T18" target="_self" title="ISOCAT_2:th.18">Th18</a></span>;<br/><a NAME="E71:39_5"/><span class="kw">then </span>
<font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c17">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A62</font></span>: <font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c27">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">b2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c27">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c27">g</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:39_5"><span class="lab"><font color="Green" title="E59">A40</font></span></a>, <a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
;<br/><a NAME="E73:39_5"/><span class="lab"><font color="Green" title="E82">A63</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c21">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:39_5"><span class="lab"><font color="Green" title="E70">A51</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A64</font></span>: <font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c19">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T47" title="CAT_2:th.47">CAT_2:47</a></span>
;<br/><a NAME="E75:39_5"/>
<span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c29">g9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c16">G2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c34">v1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:39_5"><span class="lab"><font color="Green" title="E82">A63</font></span></a>, <a class="txt" href="#E63:39_5"><span class="lab"><font color="Green" title="E76">A57</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#D4" target="_self" title="ISOCAT_2:def.4">Def4</a></span>;<br/><span class="kw">then </span><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c34">v1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c29">g9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:39_5"><span class="lab"><font color="Green" title="E55">A36</font></span></a>, <a class="ref" href="nattra_1.html#T42" title="NATTRA_1:th.42">NATTRA_1:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c32">e1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c27">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:39_5"><span class="lab"><font color="Green" title="E77">A58</font></span></a>, <a class="txt" href="#E34:39_5"><span class="lab"><font color="Green" title="E56">A37</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c27">g</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c33">e2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:39_5"><span class="lab"><font color="Green" title="E65">A46</font></span></a>, <a class="txt" href="#E35:39_5"><span class="lab"><font color="Green" title="E57">A38</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c29">g9</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">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">a1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:39_5"><span class="lab"><font color="Green" title="E60">A41</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c21">G1</font>,<font color="Maroon" title="c17">H2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c23">t1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E69:39_5"><span class="lab"><font color="Green" title="E79">A60</font></span></a>, <a class="txt" href="#E30:39_5"><span class="lab"><font color="Green" title="E53">A34</font></span></a>, <a class="ref" href="nattra_1.html#T42" title="NATTRA_1:th.42">NATTRA_1:42</a></span>
;<br/><a NAME="E77:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A65</font></span>: 
<font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c34">v1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c23">t1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/><a NAME="E78:39_5"/><span class="lab"><font color="Green" title="E85">A66</font></span>: 
<font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c16">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:39_5"><span class="lab"><font color="Green" title="E82">A63</font></span></a>, <a class="txt" href="#E63:39_5"><span class="lab"><font color="Green" title="E76">A57</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#T18" target="_self" title="ISOCAT_2:th.18">Th18</a></span>;<br/><a NAME="E79:39_5"/><span class="kw">then </span>
<font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c16">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A67</font></span>: <font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c27">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">b2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c27">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c27">g</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:39_5"><span class="lab"><font color="Green" title="E66">A47</font></span></a>, <a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
;<br/><span class="lab"><font color="Green" title="E87">A68</font></span>: <font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">ab2</font> = 
<font color="Maroon" title="c8">u9</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c14">a2</font>,<font color="Maroon" title="c15">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="txt" href="#E6:39_5"><span class="lab"><font color="Green" title="E41">A22</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">t9</font> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c14">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">b2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T2" target="_self" title="ISOCAT_2:th.2">Th2</a></span>
<br/>.= 
<font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:39_5"><span class="lab"><font color="Green" title="E44">A25</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
;<br/><a NAME="E82:39_5"/><span class="lab"><font color="Green" title="E88">A69</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c17">H2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:39_5"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E83:39_5"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c15">b2</font>,<font color="Maroon" title="c15">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c30">h9</font> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<font color="Maroon" title="c28">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></span>
;<br/><a NAME="E85:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A70</font></span>: 
<font color="Maroon" title="c24">f</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"><font color="Maroon" title="c27">g</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c15">b2</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"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c19">a1</font></span>)</span>,<font color="Maroon" title="c28">h</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="#E38:39_5"><span class="lab"><font color="Green" title="E58">A39</font></span></a>, <a class="txt" href="#E49:39_5"><span class="lab"><font color="Green" title="E63">A44</font></span></a>, <a class="txt" href="#E67:39_5"><span class="lab"><font color="Green" title="E78">A59</font></span></a>, <a class="ref" href="cat_2.html#T40" title="CAT_2:th.40">CAT_2:40</a></span>;<br/><a NAME="E86:39_5"/><span class="lab"><font color="Green" title="E90">A71</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></span>;<br/><a NAME="E87:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A72</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c17">H2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:39_5"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="ref" href="cat_1.html#T52" title="CAT_1:th.52">CAT_1:52</a></span>;<br/><span class="lab"><font color="Green" title="E92">A73</font></span>: <font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</font> = 
<font color="Maroon" title="c5">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c31">f9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</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="c22">H1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:39_5"><span class="lab"><font color="Green" title="E78">A59</font></span></a>, <a class="txt" href="#E85:39_5"><span class="lab"><font color="Green" title="E89">A70</font></span></a>, <a class="txt" href="#E72:39_5"><span class="lab"><font color="Green" title="E81">A62</font></span></a>, <a class="txt" href="#E59:39_5"><span class="lab"><font color="Green" title="E72">A53</font></span></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:39_5"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="txt" href="#E86:39_5"><span class="lab"><font color="Green" title="E90">A71</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
;<br/><a NAME="E89:39_5"/><span class="lab"><font color="Green" title="E93">A74</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c16">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:39_5"><span class="lab"><font color="Green" title="E82">A63</font></span></a>, <a class="txt" href="#E63:39_5"><span class="lab"><font color="Green" title="E76">A57</font></span></a>, <a class="txt" href="#E42:39_5"><span class="lab"><font color="Green" title="E61">A42</font></span></a>, <a class="ref" href="isocat_2.html#T18" target="_self" title="ISOCAT_2:th.18">Th18</a>, <a class="ref" href="isocat_1.html#T30" title="ISOCAT_1:th.30">ISOCAT_1:30</a></span>;<br/><a NAME="E90:39_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A75</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c16">G2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:39_5"><span class="lab"><font color="Green" title="E69">A50</font></span></a>, <a class="ref" href="cat_1.html#T52" title="CAT_1:th.52">CAT_1:52</a></span>;<br/><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</font> = 
<font color="Maroon" title="c4">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c31">f9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_5"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</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="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:39_5"><span class="lab"><font color="Green" title="E78">A59</font></span></a>, <a class="txt" href="#E85:39_5"><span class="lab"><font color="Green" title="E89">A70</font></span></a>, <a class="txt" href="#E80:39_5"><span class="lab"><font color="Green" title="E86">A67</font></span></a>, <a class="txt" href="#E74:39_5"><span class="lab"><font color="Green" title="E83">A64</font></span></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E89:39_5"><span class="lab"><font color="Green" title="E93">A74</font></span></a>, <a class="txt" href="#E56:39_5"><span class="lab"><font color="Green" title="E69">A50</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">ab2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:39_5"><span class="lab"><font color="Green" title="E51">A32</font></span></a>, <a class="txt" href="#E28:39_5"><span class="lab"><font color="Green" title="E52">A33</font></span></a>, <a class="txt" href="#E81:39_5"><span class="lab"><font color="Green" title="E87">A68</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:39_5"><span class="lab"><font color="Green" title="E88">A69</font></span></a>, <a class="txt" href="#E90:39_5"><span class="lab"><font color="Green" title="E94">A75</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c34">v1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E82:39_5"><span class="lab"><font color="Green" title="E88">A69</font></span></a>, <a class="txt" href="#E89:39_5"><span class="lab"><font color="Green" title="E93">A74</font></span></a>, <a class="txt" href="#E56:39_5"><span class="lab"><font color="Green" title="E69">A50</font></span></a>, <a class="ref" href="cat_1.html#T54" title="CAT_1:th.54">CAT_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c23">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:39_5"><span class="lab"><font color="Green" title="E43">A24</font></span></a>, <a class="txt" href="#E78:39_5"><span class="lab"><font color="Green" title="E85">A66</font></span></a>, <a class="txt" href="#E77:39_5"><span class="lab"><font color="Green" title="E84">A65</font></span></a>, <a class="ref" href="nattra_1.html#T27" title="NATTRA_1:th.27">NATTRA_1:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:39_5"><span class="lab"><font color="Green" title="E47">A28</font></span></a>, <a class="txt" href="#E70:39_5"><span class="lab"><font color="Green" title="E80">A61</font></span></a>, <a class="ref" href="nattra_1.html#T27" title="NATTRA_1:th.27">NATTRA_1:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c21">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:39_5"><span class="lab"><font color="Green" title="E69">A50</font></span></a>, <a class="txt" href="#E62:39_5"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="txt" href="#E26:39_5"><span class="lab"><font color="Green" title="E50">A31</font></span></a>, <a class="ref" href="cat_1.html#T54" title="CAT_1:th.54">CAT_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c20">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:39_5"><span class="lab"><font color="Green" title="E47">A28</font></span></a>, <a class="txt" href="#E55:39_5"><span class="lab"><font color="Green" title="E68">A49</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c35">v2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c15">b2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">H1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c28">h</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c20">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:39_5"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="txt" href="#E86:39_5"><span class="lab"><font color="Green" title="E90">A71</font></span></a>, <a class="txt" href="#E31:39_5"><span class="lab"><font color="Green" title="E54">A35</font></span></a>, <a class="ref" href="cat_1.html#T54" title="CAT_1:th.54">CAT_1:54</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</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="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:39_5"><span class="lab"><font color="Green" title="E54">A35</font></span></a>, <a class="txt" href="#E87:39_5"><span class="lab"><font color="Green" title="E91">A72</font></span></a>, <a class="txt" href="#E25:39_5"><span class="lab"><font color="Green" title="E49">A30</font></span></a>, <a class="txt" href="#E88:39_5"><span class="lab"><font color="Green" title="E92">A73</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c24">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">ab1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:39_5"><span class="lab"><font color="Green" title="E67">A48</font></span></a>, <a class="txt" href="#E4:39_5"><span class="lab"><font color="Green" title="E40">A21</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</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="E13:39"/><span class="lab"><font color="Green" title="E39">A76</font></span>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></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">u</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> st <font color="Maroon" title="c6">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Olive" title="b1">u</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">u</font> = <font color="Maroon" title="c9">u</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:39"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">u</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">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c10">u</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">s</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">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="c10">u</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c11">s</font> implies for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">s</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:39_6"/><span class="lab"><font color="Green" title="E40">A77</font></span>: 
<font color="Maroon" title="c10">u</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c11">s</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">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">s</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c12">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</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">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">s</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c12">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><a NAME="E2:39_6"/>
<font color="Maroon" title="c7">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Maroon" title="c8">u9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T1" target="_self" title="ISOCAT_2:th.1">Th1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_6"/>
<font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c12">a</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">s</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c12">a</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E1:39_6"><span class="lab"><font color="Green" title="E40">A77</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">hence </span><a NAME="E16:39"/>
<font color="Maroon" title="c6">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c10">u</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:39"><span class="lab"><font color="Green" title="E39">A76</font></span></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</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/>


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