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<b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">G1</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c6">F2</font>, <font color="Maroon" title="c7">G2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green" title="E50">A1</font></i>: 
<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">G1</font>
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green" title="E51">A2</font></i>: 
<font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font>
 ;<br/>

<a NAME="E3:55"/><i><font color="Green" title="E52">A3</font></i>: 
( <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">G1</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G2</font> )
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:55"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:55"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">t1</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">G1</font>;<br/><b>let </b><font color="Maroon" title="c9">t2</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">F2</font>,<font color="Maroon" title="c7">G2</font>;<br/><b>let </b><font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>;<br/>





<b>assume </b><a NAME="E4:55"/><i><font color="Green" title="E53">A4</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</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> 
 ;<br/>

<b>let </b><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">a</font>,<font color="Maroon" title="c11">b</font>;<br/>

<a NAME="E5:55"/><i><font color="Green" title="E54">A5</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</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="c12">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">G1</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <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"><font color="Maroon" title="c7">G2</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:55"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:55"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></i>;<br/>
<a NAME="E6:55"/><i><font color="Green" title="E55">A6</font></i>: 
<span class="p1"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="isocat_2.html#T45" target="_self" title="ISOCAT_2:th.45">Th45</a></i>;<br/>
<a NAME="E7:55"/><i><font color="Green" title="E56">A7</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">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"><span class="p2">(<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="c12">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="isocat_2.html#T42" target="_self" title="ISOCAT_2:th.42">Th42</a></i>;<br/>
<a NAME="E8:55"/><i><font color="Green" title="E57">A8</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E9:55"/><i><font color="Green" title="E58">A9</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E10:55"/><i><font color="Green" title="E59">A10</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E11:55"/><i><font color="Green" title="E60">A11</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E12:55"/><i><font color="Green" title="E61">A12</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E13:55"/><i><font color="Green" title="E62">A13</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E14:55"/><i><font color="Green" title="E63">A14</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E15:55"/><i><font color="Green" title="E64">A15</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<i><font color="Green" title="E65">A16</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> = 
<font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E8:55"><i><font color="Green" title="E57">A8</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</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="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:55"><i><font color="Green" title="E58">A9</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/>
<i><font color="Green" title="E66">A17</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> = 
<font color="Maroon" title="c6">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E11:55"><i><font color="Green" title="E60">A11</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E10:55"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/>
<a NAME="E18:55"/><i><font color="Green" title="E67">A18</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</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="c12">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</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="c12">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E8:55"><i><font color="Green" title="E57">A8</font></i></a>, <a class="txt" href="isocat_2.html#E9:55"><i><font color="Green" title="E58">A9</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>;<br/>
<a NAME="E19:55"/><i><font color="Green" title="E68">A19</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <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"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E10:55"><i><font color="Green" title="E59">A10</font></i></a>, <a class="txt" href="isocat_2.html#E11:55"><i><font color="Green" title="E60">A11</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>;<br/>
<a NAME="E20:55"/><i><font color="Green" title="E69">A20</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <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#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E12:55"><i><font color="Green" title="E61">A12</font></i></a>, <a class="txt" href="isocat_2.html#E13:55"><i><font color="Green" title="E62">A13</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>;<br/>
<a NAME="E21:55"/><i><font color="Green" title="E70">A21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <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#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E14:55"><i><font color="Green" title="E63">A14</font></i></a>, <a class="txt" href="isocat_2.html#E15:55"><i><font color="Green" title="E64">A15</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>;<br/>
<i><font color="Green" title="E71">A22</font></i>:  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> = 
<font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E12:55"><i><font color="Green" title="E61">A12</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E13:55"><i><font color="Green" title="E62">A13</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/>
<i><font color="Green" title="E72">A23</font></i>:  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span> = 
<font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E14:55"><i><font color="Green" title="E63">A14</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E15:55"><i><font color="Green" title="E64">A15</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/>
<a NAME="E24:55"/><i><font color="Green" title="E73">A24</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="isocat_2.html#T42" target="_self" title="ISOCAT_2:th.42">Th42</a></i>;<br/>
<a NAME="E25:55"/><i><font color="Green" title="E74">A25</font></i>: 
<span class="p1"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <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="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="isocat_2.html#T45" target="_self" title="ISOCAT_2:th.45">Th45</a></i>;<br/>
<a NAME="E26:55"/><i><font color="Green" title="E75">A26</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:55"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="isocat_2.html#T44" target="_self" title="ISOCAT_2:th.44">Th44</a></i>;<br/>
<a NAME="E27:55"/><b>then </b><i><font color="Green" title="E76">A27</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">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> 
 
<b>by </b><i><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E28:55"/><i><font color="Green" title="E77">A28</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E29:55"/><i><font color="Green" title="E78">A29</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:55"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/>
<a NAME="E30:55"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E26:55"><i><font color="Green" title="E75">A26</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></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"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c6">F2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E29:55"><i><font color="Green" title="E78">A29</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">G1</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">t1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">G2</font> <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#K9" title="CAT_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">t2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:55"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="isocat_2.html#E6:55"><i><font color="Green" title="E55">A6</font></i></a>, <a class="txt" href="isocat_2.html#E7:55"><i><font color="Green" title="E56">A7</font></i></a>, <a class="txt" href="isocat_2.html#E16:55"><i><font color="Green" title="E65">A16</font></i></a>, <a class="txt" href="isocat_2.html#E17:55"><i><font color="Green" title="E66">A17</font></i></a>, <a class="txt" href="isocat_2.html#E18:55"><i><font color="Green" title="E67">A18</font></i></a>, <a class="txt" href="isocat_2.html#E19:55"><i><font color="Green" title="E68">A19</font></i></a>, <a class="ref" href="cat_2.html#T39" title="CAT_2:th.39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></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#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E20:55"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="isocat_2.html#E21:55"><i><font color="Green" title="E70">A21</font></i></a>, <a class="txt" href="isocat_2.html#E22:55"><i><font color="Green" title="E71">A22</font></i></a>, <a class="txt" href="isocat_2.html#E23:55"><i><font color="Green" title="E72">A23</font></i></a>, <a class="txt" href="isocat_2.html#E24:55"><i><font color="Green" title="E73">A24</font></i></a>, <a class="txt" href="isocat_2.html#E25:55"><i><font color="Green" title="E74">A25</font></i></a>, <a class="ref" href="cat_2.html#T39" title="CAT_2:th.39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">&lt;:</a><span class="default"><font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c7">G2</font></span><a href="isocat_2.html#K10" title="ISOCAT_2:func.10">:&gt;</a></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#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">&lt;:</a><span class="default"><font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font></span><a href="isocat_2.html#K15" title="ISOCAT_2:func.15">:&gt;</a></span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E27:55"><i><font color="Green" title="E76">A27</font></i></a>, <a class="txt" href="isocat_2.html#E28:55"><i><font color="Green" title="E77">A28</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
;<br/><br/>


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