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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> 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="b2">T</font>,<font color="Olive" title="b3">D</font> holds   <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Olive" title="b4">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Olive" title="b4">F</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> 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="Olive" title="b1">T</font>,<font color="Olive" title="b2">D</font> holds   <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Olive" title="b3">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <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></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> 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="b2">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> holds   <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Olive" title="b2">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Olive" title="b2">F</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> 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> holds   <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Olive" title="b1">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <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></span><br/><b>let </b><font color="Maroon" title="c5">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">  <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Maroon" title="c5">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span><br/>









<b>reconsider </b><font color="Maroon" title="c6">F'</font> = <font color="Maroon" title="c5">F</font> as    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">T</font>, <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Maroon" title="c5">F</font> <b>by </b><i><a class="ref" href="cat_5.html#T8" title="CAT_5:th.8">CAT_5:8</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">T'</font> being    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font>;<br/>
<a NAME="E3:70"/><i><font color="Green" title="E35">A1</font></i>: 
 <a href="index_1.html#K16" title="INDEX_1:func.16">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c7">T'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="index_1.html#D12" target="_self" title="INDEX_1:def.12">Def12</a></i>;<br/>
<font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font> = 
<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>
<b>by </b><i><a class="ref" href="index_1.html#T27" target="_self" title="INDEX_1:th.27">Th27</a></i>
<br/>.= 
<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/>
<a NAME="E5:70"/><b>then </b>
 <a href="index_1.html#K16" title="INDEX_1:func.16">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K21" title="INDEX_1:func.21">*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <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>
 
<b>by </b><i><a class="txt" href="index_1.html#E3:70"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="index_1.html#T18" target="_self" title="INDEX_1:th.18">Th18</a>, <a class="ref" href="cat_5.html#T22" title="CAT_5:th.22">CAT_5:22</a></i>;<br/>
<b>hence </b><a NAME="E6:70"/>
 <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <font color="Maroon" title="c5">F</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c5">F</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#T14" target="_self" title="INDEX_1:th.14">Th14</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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