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<span class="kw">set </span><font color="Maroon" title="c7">G1</font> = <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">G2</font> = <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span>;<br/>
<a NAME="E1:83_1_1"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font>, <a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>), <a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>) <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T48" target="_self" onmouseover="rs('cat_8/T48')" onmouseout="rh()">Th48</a></span>;<br/>
<a NAME="E2:83_1_1"/>
( <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> 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="#E1:83"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="cat_6.html#T35" onmouseover="rs('cat_6/T35')" onmouseout="rh()">CAT_6:35</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">H2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:83_1_1"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
( <font color="Maroon" title="c9">H2</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_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> &amp; (  for <font color="Olive" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font></span>)</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_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</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="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</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="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> holds <br/><font color="Maroon" title="c9">H2</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="#E1:83_1_1"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="cat_8.html#D17" target="_self" onmouseover="rs('cat_8/D17')" onmouseout="rh()">Def17</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:83_1_1"/>
 ex <font color="Olive" title="b1">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font></span>)</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; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83_1_1"><span class="lab"><font color="Green" title="E44">A3</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">  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font></span>)</span>  st <font color="Olive">b<sub>1</sub></font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c10">H3</font>, <font color="Maroon" title="c11">H4</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c2">C2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">D1</font> <a href="cat_8.html#K8" title="CAT_8:func.8">[x]</a> <font color="Maroon" title="c4">D2</font></span>)</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="c10">H3</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H3</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H3</font> &amp; <font color="Maroon" title="c11">H4</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</font> implies <font color="Maroon" title="c10">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">H4</font> )</span><br/>

<span class="kw">assume </span><a NAME="E6:83_1_1"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
( <font color="Maroon" title="c10">H3</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H3</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H3</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"> (  not <font color="Maroon" title="c11">H4</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  or  not <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</font> or  not <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</font> or <font color="Maroon" title="c10">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">H4</font> )</span><br/>

<span class="kw">assume </span><a NAME="E7:83_1_1"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
( <font color="Maroon" title="c11">H4</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">F1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K9" title="CAT_8:func.9">pr1</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</font> &amp; <font color="Maroon" title="c6">F2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="cat_8.html#K10" title="CAT_8:func.10">pr2</a> (<font color="Maroon" title="c3">D1</font>,<font color="Maroon" title="c4">D2</font>)</span>)</span> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c11">H4</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="c10">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">H4</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c10">H3</font> = 
<font color="Maroon" title="c9">H2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:83_1_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="txt" href="#E4:83_1_1"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c11">H4</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:83_1_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E4:83_1_1"><span class="lab"><font color="Green" title="E44">A3</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/>


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