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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="firebrick">::  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 <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> 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 <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font><br/>  for <font color="Olive" title="b4">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 <br/> ( <font color="Olive" title="b1">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b4">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b4">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b1">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b2">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b4">a</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="firebrick">::  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> 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 <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/>  for <font color="Olive" title="b2">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 <br/> ( <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E14">A1</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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 <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/>  for <font color="Olive" title="b2">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 <br/> ( <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b2">a</font> )</span><br/>

<a NAME="E2:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A2</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>
 
<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">let </span><font color="Maroon" title="c6">u</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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 <br/> ( <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b1">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b1">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Olive" title="b1">a</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> )</span><br/>



<a NAME="E3:15"/>
 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#T23" title="CAT_2:th.23">CAT_2:23</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">t</font> = <font color="Maroon" title="c6">u</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#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> ;<br/>
<a NAME="E5:15"/><span class="lab"><font color="Green" title="E16">A3</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="c7">a</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <span class="comment"><font color="firebrick">:: 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="firebrick">::  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"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</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/>

<a NAME="E1:15_1"/>
( <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c9">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="ref" href="isocat_2.html#T10" target="_self" title="ISOCAT_2:th.10">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:15_1"/>
 not  <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"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E17">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</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"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>)</span><br/><a NAME="E1:15_2"/><span class="lab"><font color="Green" title="E18">A5</font></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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c9">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="ref" href="isocat_2.html#T10" target="_self" title="ISOCAT_2:th.10">Th12</a></span>;<br/><a NAME="E2:15_2"/><span class="lab"><font color="Green" title="E19">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"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">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="#E5:15"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> = 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</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="E4:15_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</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"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_2"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E2:15_2"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="cat_1.html#D4" title="CAT_1:def.4">CAT_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span><br/><a NAME="E1:15_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</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"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E17">A4</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E2:15_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D4" title="CAT_1:def.4">CAT_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">s</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font> as    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="nattra_1.html#D3" title="NATTRA_1:def.3">NATTRA_1:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E18">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">b2</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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>  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="c10">b1</font>,<font color="Maroon" title="c11">b2</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <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"><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="c7">a</font></span>)</span> <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">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:15_4"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c10">b1</font>,<font color="Maroon" title="c11">b2</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <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"><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="c7">a</font></span>)</span> <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">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span></span><br/><a NAME="E2:15_4"/><span class="lab"><font color="Green" title="E20">A9</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"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>,<span class="p1">(<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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">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="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c12">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">b2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">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">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span></span><br/><a NAME="E3:15_4"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c7">a</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#T27" title="CAT_1:th.27">CAT_1:27</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">g</font> = <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="c7">a</font></span>)</span>,<font color="Maroon" title="c12">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">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="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></span>;<br/><a NAME="E5:15_4"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:15_4"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="isocat_2.html#T11" target="_self" title="ISOCAT_2:th.11">Th13</a></span>;<br/><a NAME="E6:15_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A12</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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/><span class="lab"><font color="Green" title="E24">A13</font></span>: <font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</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="E8:15_4"/><span class="lab"><font color="Green" title="E25">A14</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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</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="E9:15_4"/><span class="lab"><font color="Green" title="E26">A15</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"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>,<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">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="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/><a NAME="E10:15_4"/><span class="lab"><font color="Green" title="E27">A16</font></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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c10">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="ref" href="isocat_2.html#T10" target="_self" title="ISOCAT_2:th.10">Th12</a></span>;<br/><a NAME="E11:15_4"/><span class="lab"><font color="Green" title="E28">A17</font></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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <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="c7">a</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c11">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c7">a</font>,<font color="Maroon" title="c11">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="isocat_2.html#T10" target="_self" title="ISOCAT_2:th.10">Th12</a></span>;<br/><a NAME="E12:15_4"/><span class="lab"><font color="Green" title="E29">A18</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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</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="E13:15_4"/><span class="lab"><font color="Green" title="E30">A19</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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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="#E5:15_4"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="cat_1.html#T84" title="CAT_1:th.84">CAT_1:84</a></span>;<br/><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">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="#E2:15"><span class="lab"><font color="Green" title="E15">A2</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><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15_4"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E2:15_4"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E11:15_4"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></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="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</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">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c12">f</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T36" title="CAT_2:th.36">CAT_2:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_4"><span class="lab"><font color="Green" title="E22">A11</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">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_4"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E8:15_4"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</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="c13">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">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E5:15_4"><span class="lab"><font color="Green" title="E22">A11</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"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:15_4"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E13:15_4"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> (<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c12">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="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_4"><span class="lab"><font color="Green" title="E22">A11</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"><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="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T36" title="CAT_2:th.36">CAT_2:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">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">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_4"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E7:15_4"><span class="lab"><font color="Green" title="E24">A13</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"><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="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">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">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:15_4"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E9:15_4"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E10:15_4"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:15"/>
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E16">A3</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="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span><br/>

<span class="kw">hence </span><a NAME="E11:15"/>
<span class="p1">(<span class="default"><a href="funct_5.html#K1" title="FUNCT_5:func.1">curry</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
