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<span class="kw">reconsider </span><font color="Maroon" title="c3">X2</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" onmouseover="rs('tarski/T1')" onmouseout="rh()">TARSKI:1</a></span>;<br/>
<a NAME="E2:109_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">T</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> is   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>, <font color="Olive" title="b3">T</font> is    <a href="cat_8.html#M3" title="CAT_8:mode.3">natural_transformation</a> of <font color="Olive" title="b1">F2</font>,<font color="Olive" title="b2">F1</font> : ( <font color="Olive" title="b1">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">F2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">F1</font> <a href="cat_8.html#R4" title="CAT_8:pred.4">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#D28" target="_self" onmouseover="rs('cat_8/D28')" onmouseout="rh()">Def28</a></span>;<br/>
<a NAME="E3:109_1_1"/><span class="kw">then </span>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">X2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">x2</font>,<font color="Olive" title="b1">x1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">x3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> :  ex <font color="Olive" title="b4">F1</font>, <font color="Olive" title="b5">F2</font>, <font color="Olive" title="b6">F3</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> ex <font color="Olive" title="b7">T1</font> being    <a href="cat_8.html#M3" title="CAT_8:mode.3">natural_transformation</a> of <font color="Olive" title="b4">F1</font>,<font color="Olive" title="b5">F2</font> ex <font color="Olive" title="b8">T2</font> being    <a href="cat_8.html#M3" title="CAT_8:mode.3">natural_transformation</a> of <font color="Olive" title="b5">F2</font>,<font color="Olive" title="b6">F3</font> st <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">F1</font>,<font color="Olive" title="b5">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b7">T1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">F2</font>,<font color="Olive" title="b6">F3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b8">T2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">F1</font>,<font color="Olive" title="b6">F3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b8">T2</font> <a href="cat_8.html#K13" title="CAT_8:func.13">`*`</a> <font color="Olive" title="b7">T1</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c3">X2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c3">X2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="cat_8.html#E94"><span class="lab"><font color="Green" title="E60">Lm5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:109_1_1"/>
(  not  <a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>) is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  <a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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