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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</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><br/> for <font color="Olive" title="b2">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Olive" title="b2">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b3">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">F</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c5">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c5">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c6">b</font></span>)</span></span><br/>











<a NAME="E1:21"/>
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">G</font> = <font color="Maroon" title="c4">F</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Ff</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c5">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<a NAME="E4:21"/>
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="isocat_2.html#T18" target="_self" title="ISOCAT_2:th.18">Th18</a></i>;<br/>
<a NAME="E5:21"/><b>then </b>
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="isocat_2.html#K4" title="ISOCAT_2:func.4">?-</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">b</font>
<b>by </b><i><a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c8">Ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c6">b</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c5">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c6">b</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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