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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="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">C</font> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c1">C</font></span><br/>

<span class="kw">thus </span><a NAME="E1:23"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_2.html#D4" target="_self" title="CAT_2:def.4">CAT_2:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b9</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a9</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> holds <br/> <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b3">a9</font>,<font color="Olive" title="b4">b9</font>) ) &amp;  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> &amp; (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a9</font> holds <br/> <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b2">a9</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E2:23"/>
( (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b9</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a9</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b9</font> holds <br/> <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b3">a9</font>,<font color="Olive" title="b4">b9</font>) ) &amp;  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> &amp; (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a9</font> holds <br/> <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b2">a9</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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