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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">C1</font>, <font color="Maroon" title="c3">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">  for <font color="Olive" title="b1">F1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c1">C</font><br/>  for <font color="Olive" title="b2">F2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">C2</font>,<font color="Maroon" title="c1">C</font>  st <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>  holds <br/>(  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c1">C</font>; <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">  for <font color="Olive" title="b1">F2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">C2</font>,<font color="Maroon" title="c1">C</font>  st <font color="Maroon" title="c4">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">F2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  holds <br/>(  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Olive" title="b1">F2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">F2</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">C2</font>,<font color="Maroon" title="c1">C</font>; <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"> ( <font color="Maroon" title="c4">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  implies (  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:87"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
( <font color="Maroon" title="c4">F1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</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_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">T</font> =  the    <a href="cat_7.html#M2" title="CAT_7:mode.2">pullback</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">D0</font> being   <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a>, <font color="Maroon" title="c8">P01</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c2">C1</font>, <font color="Maroon" title="c9">P02</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c3">C2</font><span class="kw"> such that </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
(  the    <a href="cat_7.html#M2" title="CAT_7:mode.2">pullback</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c8">P01</font>,<font color="Maroon" title="c9">P02</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Maroon" title="c8">P01</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c9">P02</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c8">P01</font>,<font color="Maroon" title="c9">P02</font> <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D21" target="_self" onmouseover="rs('cat_7/D21')" onmouseout="rh()">Def21</a></span>;<br/>
<a NAME="E4:87"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
( <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">P01</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">P02</font> &amp; (  for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c7">D0</font> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">P01</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Maroon" title="c9">P02</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c7">D0</font>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">P01</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <font color="Maroon" title="c9">P02</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) ) ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cat_7.html#D20" target="_self" onmouseover="rs('cat_7/D20')" onmouseout="rh()">Def20</a></span>;<br/>
<a NAME="E5:87"/><span class="lab"><font color="Green" title="E53">A4</font></span>: 
( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c8">P01</font>,<font color="Maroon" title="c9">P02</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="xtuple_0.html#K4" title="XTUPLE_0:func.4">`1_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">D0</font> &amp; <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c8">P01</font>,<font color="Maroon" title="c9">P02</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="xtuple_0.html#K5" title="XTUPLE_0:func.5">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">P01</font> &amp; <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c7">D0</font>,<font color="Maroon" title="c8">P01</font>,<font color="Maroon" title="c9">P02</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="xtuple_0.html#NK6" title="XTUPLE_0:NK.6">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P02</font> )
 
;<br/>
<a NAME="E6:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A5</font></span>: 
<font color="Maroon" title="c7">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cat_7.html#D22" target="_self" onmouseover="rs('cat_7/D22')" onmouseout="rh()">Def22</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">P1</font> = <font color="Maroon" title="c8">P01</font> as   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>,<font color="Maroon" title="c2">C1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">P2</font> = <font color="Maroon" title="c9">P02</font> as   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>,<font color="Maroon" title="c3">C2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a></span>;<br/>
<a NAME="E9:87"/>
(  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) ) ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="87_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:87_1"/><span class="lab"><font color="Green" title="E55">A6</font></span>: 
 <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D23" target="_self" onmouseover="rs('cat_7/D23')" onmouseout="rh()">Def23</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"> (  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E2:87_1"/><span class="lab"><font color="Green" title="E56">A7</font></span>: 
 <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D24" target="_self" onmouseover="rs('cat_7/D24')" onmouseout="rh()">Def24</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"> ( <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) ) ) )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c4">F1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87_1"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c8">P01</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c4">F1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D23" target="_self" onmouseover="rs('cat_7/D23')" onmouseout="rh()">Def23</a></span>
<br/>.= 
<font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c8">P01</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c9">P02</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c5">F2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E4:87"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c5">F2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D24" target="_self" onmouseover="rs('cat_7/D24')" onmouseout="rh()">Def24</a></span>
<br/>.= 
<font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:87_1"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</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">  for <font color="Olive" title="b1">D1</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b2">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b2">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">G2</font> holds <br/> ex <font color="Olive" title="b4">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b4">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> &amp; (  for <font color="Olive" title="b5">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b5">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b5">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">G2</font> holds <br/><font color="Olive" title="b4">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">H1</font> ) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c12">D1</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">  for <font color="Olive" title="b1">G1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b2">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b1">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">G2</font> 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="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></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; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G2</font> &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="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b4">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">G2</font> 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><br/><span class="kw">let </span><font color="Maroon" title="c13">G1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c2">C1</font>; <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">  for <font color="Olive" title="b1">G2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c3">C2</font>  st <font color="Maroon" title="c13">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c13">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">G2</font> holds <br/> ex <font color="Olive" title="b2">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b2">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G2</font> &amp; (  for <font color="Olive" title="b3">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b3">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">G2</font> holds <br/><font color="Olive" title="b2">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">H1</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c14">G2</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c3">C2</font>; <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"> ( <font color="Maroon" title="c13">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c14">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c13">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c14">G2</font> implies  ex <font color="Olive" title="b1">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b1">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b2">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">H1</font> ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E4:87_1"/>
( <font color="Maroon" title="c13">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c14">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c13">G1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c14">G2</font> )
 ; <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">  ex <font color="Olive" title="b1">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> st <br/>( <font color="Olive" title="b1">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b2">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b2">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Olive" title="b1">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b2">H1</font> ) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">H0</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c7">D0</font><span class="kw"> such that </span><br/><a NAME="E6:87_1"/><span class="lab"><font color="Green" title="E57">A8</font></span>: 
( <font color="Maroon" title="c15">H0</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">P01</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c15">H0</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <font color="Maroon" title="c9">P02</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c15">H0</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c7">D0</font>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">P01</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <font color="Maroon" title="c9">P02</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Maroon" title="c15">H0</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cat_7.html#D20" target="_self" onmouseover="rs('cat_7/D20')" onmouseout="rh()">Def20</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">H</font> = <font color="Maroon" title="c15">H0</font> as   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c16">H</font>
; <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"> ( <font color="Maroon" title="c16">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E8:87_1"/>
<font color="Maroon" title="c16">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></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"> ( <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> = 
<font color="Maroon" title="c16">H</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E1:87_1"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c15">H0</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c8">P01</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D23" target="_self" onmouseover="rs('cat_7/D23')" onmouseout="rh()">Def23</a></span>
<br/>.= 
<font color="Maroon" title="c13">G1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</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"> ( <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font> ) )</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c16">H</font> = 
<font color="Maroon" title="c16">H</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E2:87_1"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c15">H0</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c9">P02</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D24" target="_self" onmouseover="rs('cat_7/D24')" onmouseout="rh()">Def24</a></span>
<br/>.= 
<font color="Maroon" title="c14">G2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</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">  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>  st <font color="Olive" title="b1">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> holds <br/><font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">H1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c17">H1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</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"> ( <font color="Maroon" title="c17">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c17">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c17">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> implies <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c17">H1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E11:87_1"/><span class="lab"><font color="Green" title="E58">A9</font></span>: 
( <font color="Maroon" title="c17">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c17">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">G1</font> &amp; <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c17">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c14">G2</font> )
 ; <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"> <font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c17">H1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c18">H01</font> = <font color="Maroon" title="c17">H1</font> as   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c12">D1</font>,<font color="Maroon" title="c7">D0</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E59">A10</font></span>: <font color="Maroon" title="c8">P01</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c18">H01</font> = 
<font color="Maroon" title="c18">H01</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c8">P01</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E11:87_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c17">H1</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D23" target="_self" onmouseover="rs('cat_7/D23')" onmouseout="rh()">Def23</a></span>
<br/>.= 
<font color="Maroon" title="c13">G1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:87_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E1:87_1"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
;<br/>
<font color="Maroon" title="c9">P02</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c18">H01</font> = 
<font color="Maroon" title="c18">H01</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c9">P02</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E11:87_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
<br/>.= 
<font color="Maroon" title="c17">H1</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D24" target="_self" onmouseover="rs('cat_7/D24')" onmouseout="rh()">Def24</a></span>
<br/>.= 
<font color="Maroon" title="c14">G2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:87_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E2:87_1"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="ref" href="cat_6.html#D27" onmouseover="rs('cat_6/D27')" onmouseout="rh()">CAT_6:def 27</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E15:87_1"/>
<font color="Maroon" title="c16">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c17">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E11:87_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E13:87_1"><span class="lab"><font color="Green" title="E59">A10</font></span></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>
<span class="kw">hence </span><a NAME="E10:87"/>
(  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#D20" target="_self" onmouseover="rs('cat_7/D20')" onmouseout="rh()">Def20</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>
