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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><br/> for <font color="Olive" title="b5">J</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Olive" title="b3">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b5">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Olive" title="b1">I</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><br/> for <font color="Olive" title="b4">J</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Olive" title="b2">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><br/> for <font color="Olive" title="b3">J</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Olive" title="b1">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">J</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c4">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">J</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c4">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">J</font> be   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c4">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/>











<a NAME="E1:79"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
( <font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-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#K17" title="INDEX_1:func.17">-indexing_of</a> <font color="Maroon" title="c1">C</font> &amp;  <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">D</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D17" target="_self" title="INDEX_1:def.17">Def17</a></span>;<br/>
<a NAME="E2:79"/>
<font color="Maroon" title="c4">D</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#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#T29" target="_self" title="INDEX_1:th.29">Th29</a></span>;<br/>
<a NAME="E3:79"/><span class="kw">then </span>
 <a href="index_1.html#K14" title="INDEX_1:func.14">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#T14" target="_self" title="INDEX_1:th.14">Th14</a></span>;<br/>
<a NAME="E4:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A2</font></span>: 
 <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#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="index_1.html#K14" title="INDEX_1:func.14">rng</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_5.html#T4" title="CAT_5:th.4">CAT_5:4</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c6">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c2">I</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#T32" target="_self" title="INDEX_1:th.32">Th32</a></span>
<br/>.= 
<font color="Maroon" title="c6">J</font> <a href="index_1.html#K18" title="INDEX_1:func.18">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#T26" target="_self" title="INDEX_1:th.26">Th26</a></span>
<br/>.= 
<font color="Maroon" title="c6">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="index_1.html#K19" title="INDEX_1:func.19">*</a> <font color="Maroon" title="c2">I</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="index_1.html#T18" target="_self" title="INDEX_1:th.18">Th18</a>, <a class="ref" href="index_1.html#T22" target="_self" title="INDEX_1:th.22">Th22</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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