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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/><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_6.html#NR4" title="CAT_6:NR.4">~=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Olive" title="b2">F2</font>,<font color="Olive" title="b1">F1</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span></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/><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_6.html#NR4" title="CAT_6:NR.4">~=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Olive" title="b1">F2</font>,<font color="Maroon" title="c4">F1</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span></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 <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_6.html#NR4" title="CAT_6:NR.4">~=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:88"/><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"> <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_6.html#NR4" title="CAT_6:NR.4">~=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span></span><br/>

<a NAME="E2:88"/><span class="lab"><font color="Green" title="E51">A2</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>  &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="#E1:88"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#T52" target="_self" onmouseover="rs('cat_7/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E3:88"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
(  <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</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="c5">F2</font>,<font color="Maroon" title="c4">F1</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="c5">F2</font>,<font color="Maroon" title="c4">F1</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="c5">F2</font>,<font color="Maroon" title="c4">F1</font>), <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font>) <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#T52" target="_self" onmouseover="rs('cat_7/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E4:88"/><span class="kw">then </span>
<span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font></span><a href="cat_7.html#K8" title="CAT_7:func.8">|]</a></span>, <a href="cat_7.html#K10" title="CAT_7:func.10">pr2</a> (<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</font>), <a href="cat_7.html#K9" title="CAT_7:func.9">pr1</a> (<font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</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="#E1:88"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cat_7.html#T47" target="_self" onmouseover="rs('cat_7/T47')" onmouseout="rh()">Th47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:88"/>
<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_6.html#NR4" title="CAT_6:NR.4">~=</a> <span class="p1"><a href="cat_7.html#K8" title="CAT_7:func.8">[|</a><span class="default"><font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c4">F1</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="#E1:88"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E2:88"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E3:88"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="cat_7.html#T46" target="_self" onmouseover="rs('cat_7/T46')" onmouseout="rh()">Th46</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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