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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">F1</font>, <font color="Olive" title="b2">F2</font> being   <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>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_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#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font><br/> for <font color="Olive" title="b4">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><br/> for <font color="Olive" title="b5">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  <span class="p1">(<span class="default"><font color="Olive" title="b4">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b5">a</font></span>)</span></span><br/><b>let </b><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 <font color="Maroon" title="c1">A</font>,<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"> ( <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> implies for <font color="Olive" title="b1">t</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><br/> for <font color="Olive" title="b3">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  <span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E18">A1</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">F2</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">t</font> being   <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><br/> for <font color="Olive" title="b3">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  <span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">a</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c6">t</font> be    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>; <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">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><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  <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c7">G</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <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">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  <span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c8">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span></span><br/>





<a NAME="E2:27"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c8">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="#E1:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="isocat_1.html#K2" title="ISOCAT_1:func.2">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="isocat_1.html#T8" target="_self" title="ISOCAT_1:th.8">Th8</a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="isocat_1.html#D5" target="_self" title="ISOCAT_1:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c7">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</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="c7">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c7">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:27"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></i>
; <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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