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<b>let </b><font color="Maroon" title="c1">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">I</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">T</font> being   <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Olive" title="b1">I</font><br/> for <font color="Olive" title="b3">D</font>, <font color="Olive" title="b4">E</font> being <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/> for <font color="Olive" title="b5">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b2">T</font>,<font color="Olive" title="b3">D</font><br/> for <font color="Olive" title="b6">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b2">T</font>,<font color="Olive" title="b4">E</font>  st <font color="Olive" title="b5">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b6">G</font> holds <br/><font color="Olive" title="b5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Olive" title="b1">I</font></span><br/><b>let </b><font color="Maroon" title="c2">I</font> be   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">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">T</font> being   <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c2">I</font><br/> for <font color="Olive" title="b2">D</font>, <font color="Olive" title="b3">E</font> being <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/> for <font color="Olive" title="b4">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">D</font><br/> for <font color="Olive" title="b5">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Olive" title="b1">T</font>,<font color="Olive" title="b3">E</font>  st <font color="Olive" title="b4">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">G</font> holds <br/><font color="Olive" title="b4">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span><br/><b>let </b><font color="Maroon" title="c3">T</font> be    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c2">I</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">D</font>, <font color="Olive" title="b2">E</font> being <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/> for <font color="Olive" title="b3">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">T</font>,<font color="Olive" title="b1">D</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="c3">T</font>,<font color="Olive" title="b2">E</font>  st <font color="Olive" title="b3">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">G</font> holds <br/><font color="Olive" title="b3">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span><br/><b>let </b><font color="Maroon" title="c4">D</font>, <font color="Maroon" title="c5">E</font> be  <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> <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 <font color="Maroon" title="c3">T</font>,<font color="Maroon" title="c4">D</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="c3">T</font>,<font color="Maroon" title="c5">E</font>  st <font color="Olive" title="b1">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">G</font> holds <br/><font color="Olive" title="b1">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span><br/><b>let </b><font color="Maroon" title="c6">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">T</font>,<font color="Maroon" title="c4">D</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="c3">T</font>,<font color="Maroon" title="c5">E</font>  st <font color="Maroon" title="c6">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">G</font> holds <br/><font color="Maroon" title="c6">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></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="c3">T</font>,<font color="Maroon" title="c5">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c7">G</font> implies <font color="Maroon" title="c6">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> )</span><br/>











<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c6">F</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c7">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span><br/>

<b>thus </b><font color="Maroon" title="c6">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="index_1.html#K19" title="INDEX_1:func.19">-indexing_of</a> <font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="ref" href="index_1.html#D17" target="_self" title="INDEX_1:def.17">Def17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="index_1.html#K19" title="INDEX_1:func.19">-indexing_of</a> <font color="Maroon" title="c1">C</font>
<b>by </b><i><a class="txt" href="index_1.html#E1:69"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="index_1.html#T2" target="_self" title="INDEX_1:th.2">Th2</a></i>
<br/>.= 
<font color="Maroon" title="c7">G</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font>
<b>by </b><i><a class="ref" href="index_1.html#D17" target="_self" title="INDEX_1:def.17">Def17</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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