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<span class="kw">let </span><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font>, <font color="Maroon" title="c3">D</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">P1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">C1</font><br/>  for <font color="Olive" title="b2">P2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">C2</font>  st <font color="Olive" title="b1">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b2">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c3">D</font>,<font color="Olive" title="b1">P1</font>,<font color="Olive" title="b2">P2</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> holds <br/><font color="Maroon" title="c3">D</font>,<font color="Olive" title="b2">P2</font>,<font color="Olive" title="b1">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">P1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">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">P2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">C2</font>  st <font color="Maroon" title="c4">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">P1</font>,<font color="Olive" title="b1">P2</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> holds <br/><font color="Maroon" title="c3">D</font>,<font color="Olive" title="b1">P2</font>,<font color="Maroon" title="c4">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">P2</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">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="c4">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> implies <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c4">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:71"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
( <font color="Maroon" title="c4">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</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"> (  not <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> or <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c4">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:71"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c4">P1</font>,<font color="Maroon" title="c5">P2</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">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="c3">D</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c4">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font></span><br/>

<a NAME="E3:71"/>
 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">C2</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="c1">C1</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>  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="c3">D</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="c5">P2</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="c4">P1</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="c3">D</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="c5">P2</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="c4">P1</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> ) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="71_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">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="c6">D1</font>,<font color="Maroon" title="c2">C2</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="c6">D1</font>,<font color="Maroon" title="c1">C1</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>  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="c6">D1</font>,<font color="Maroon" title="c3">D</font> st <br/>( <font color="Olive" title="b3">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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; <font color="Maroon" title="c4">P1</font> <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="c6">D1</font>,<font color="Maroon" title="c3">D</font>  st <font color="Olive" title="b4">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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; <font color="Maroon" title="c4">P1</font> <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="c7">G1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D1</font>,<font color="Maroon" title="c2">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">  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="c6">D1</font>,<font color="Maroon" title="c1">C1</font>  st <font color="Maroon" title="c7">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>  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="c6">D1</font>,<font color="Maroon" title="c3">D</font> st <br/>( <font color="Olive" title="b2">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c6">D1</font>,<font color="Maroon" title="c3">D</font>  st <font color="Olive" title="b3">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c8">G2</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D1</font>,<font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c7">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">G2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  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="c6">D1</font>,<font color="Maroon" title="c3">D</font> 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">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c8">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="c6">D1</font>,<font color="Maroon" title="c3">D</font>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c8">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="E1:71_1"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
( <font color="Maroon" title="c7">G1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">G2</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">  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="c6">D1</font>,<font color="Maroon" title="c3">D</font> 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">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c8">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="c6">D1</font>,<font color="Maroon" title="c3">D</font>  st <font color="Olive" title="b2">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <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="c8">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">consider </span><font color="Maroon" title="c9">H</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D1</font>,<font color="Maroon" title="c3">D</font><span class="kw"> such that </span><br/><a NAME="E3:71_1"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
( <font color="Maroon" title="c9">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c4">P1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c5">P2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G1</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="c6">D1</font>,<font color="Maroon" title="c3">D</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="c4">P1</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="c8">G2</font> &amp; <font color="Maroon" title="c5">P2</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="c7">G1</font> holds <br/><font color="Maroon" title="c9">H</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="#E1:71_1"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E38">A1</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">take </span>
<font color="Maroon" title="c9">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="c9">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">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="c6">D1</font>,<font color="Maroon" title="c3">D</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="c5">P2</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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</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="c8">G2</font> holds <br/><font color="Maroon" title="c9">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="E4:71_1"/>
( <font color="Maroon" title="c9">H</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">G2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71_1"><span class="lab"><font color="Green" title="E41">A4</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" title="b1">H1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D1</font>,<font color="Maroon" title="c3">D</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="c5">P2</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="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</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="c8">G2</font> holds <br/><font color="Maroon" title="c9">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="c10">H1</font> be   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D1</font>,<font color="Maroon" title="c3">D</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">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">G2</font> implies <font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c10">H1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:71_1"/>
( <font color="Maroon" title="c10">H1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c5">P2</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">G1</font> &amp; <font color="Maroon" title="c4">P1</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Maroon" title="c10">H1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c8">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="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c10">H1</font></span><br/>

<span class="kw">hence </span><a NAME="E6:71_1"/>
<font color="Maroon" title="c9">H</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c10">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71_1"><span class="lab"><font color="Green" title="E41">A4</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="E4:71"/>
<font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">P2</font>,<font color="Maroon" title="c4">P1</font> <a href="cat_8.html#R2" title="CAT_8:pred.2">is_product_of</a> <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c1">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="cat_8.html#D17" target="_self" onmouseover="rs('cat_8/D17')" onmouseout="rh()">Def17</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>
