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<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</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">  <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="140_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:140_1"/>
( <font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or ( <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) or (  not <font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="140_1_1"><span class="kw">suppose </span></a><a NAME="E1:140_1_1"/>
<font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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">  <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:140_1_1"/>
 <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T28" target="_self" onmouseover="rs('cat_8/T28')" onmouseout="rh()">Th28</a></span>; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="140_1_2"><span class="kw">suppose </span></a><a NAME="E1:140_1_2"/>
( <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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">  <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:140_1_2"/>
 <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_7.html#T13" onmouseover="rs('cat_7/T13')" onmouseout="rh()">CAT_7:13</a></span>; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="140_1_3"><span class="kw">suppose </span></a><a NAME="E1:140_1_3"/><span class="lab"><font color="Green" title="E79">A1</font></span>: 
(  not <font color="Maroon" title="c1">C1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">C2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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">  <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font></span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c3">C</font> =  <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>);<br/><span class="kw">consider </span><font color="Maroon" title="c4">E</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><span class="p2">(<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="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<font color="Maroon" title="c2">C2</font><span class="kw"> such that </span><br/><a NAME="E3:140_1_3"/><span class="lab"><font color="Green" title="E80">A2</font></span>: 
<font color="Maroon" title="c4">E</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 <span class="kw">and </span><br/><a NAME="E4:140_1_3"/><span class="lab"><font color="Green" title="E81">A3</font></span>: 
 for <font color="Olive" title="b1">D</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">D</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c1">C1</font></span>)</span>,<font color="Maroon" title="c2">C2</font>  st <font color="Olive" title="b2">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/> ex <font color="Olive" title="b3">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<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> st <br/>( <font color="Olive" title="b3">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">E</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="cat_8.html#K11" title="CAT_8:func.11">[x]</a> <span class="p2">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C1</font></span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b4">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<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>  st <font color="Olive" title="b4">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">E</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">H1</font> <a href="cat_8.html#K11" title="CAT_8:func.11">[x]</a> <span class="p2">(<span class="default"><a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Maroon" title="c1">C1</font></span>)</span></span>)</span> holds <br/><font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">H1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:140_1_3"><span class="lab"><font color="Green" title="E79">A1</font></span></a>, <a class="txt" href="cat_8.html#E111"><span class="lab"><font color="Green" title="E73">Lm6</font></span></a></span>;<br/><a NAME="E5:140_1_3"/><span class="lab"><font color="Green" title="E82">A4</font></span>: 
 <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>),<font color="Maroon" title="c4">E</font> <a href="cat_8.html#R6" title="CAT_8:pred.6">is_exponent_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:140_1_3"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E4:140_1_3"><span class="lab"><font color="Green" title="E81">A3</font></span></a>, <a class="ref" href="cat_8.html#D34" target="_self" onmouseover="rs('cat_8/D34')" onmouseout="rh()">Def34</a></span>;<br/><a NAME="E6:140_1_3"/>
<font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font>, <a href="cat_8.html#K18" title="CAT_8:func.18">eval</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>) <a href="cat_8.html#R6" title="CAT_8:pred.6">is_exponent_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T72" target="_self" onmouseover="rs('cat_8/T72')" onmouseout="rh()">Th72</a></span>;<br/><span class="kw">hence </span><a NAME="E7:140_1_3"/>
 <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>) <a href="cat_6.html#NR4" title="CAT_6:NR.4">~=</a> <font color="Maroon" title="c2">C2</font> <a href="cat_8.html#K17" title="CAT_8:func.17">|^</a> <font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:140_1_3"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E5:140_1_3"><span class="lab"><font color="Green" title="E82">A4</font></span></a>, <a class="ref" href="cat_8.html#T73" target="_self" onmouseover="rs('cat_8/T73')" onmouseout="rh()">Th73</a></span>; <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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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