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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> holds <br/> (  <a href="isocat_2.html#K9" title="ISOCAT_2:func.9">Pr1</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">F</font> &amp;  <a href="isocat_2.html#K10" title="ISOCAT_2:func.10">Pr2</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">G</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font> holds <br/> (  <a href="isocat_2.html#K9" title="ISOCAT_2:func.9">Pr1</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="isocat_2.html#K10" title="ISOCAT_2:func.10">Pr2</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Olive" title="b1">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">G</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="isocat_2.html#K9" title="ISOCAT_2:func.9">Pr1</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="isocat_2.html#K10" title="ISOCAT_2:func.10">Pr2</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">G</font> )</span><br/>









<span class="kw">thus </span> <a href="isocat_2.html#K9" title="ISOCAT_2:func.9">Pr1</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> = 
<span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#D10" title="CAT_2:def.10">CAT_2:def 10</a></span>
<br/>.= 
<font color="Maroon" title="c4">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T82" title="FUNCT_3:th.82">FUNCT_3:82</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="isocat_2.html#K10" title="ISOCAT_2:func.10">Pr2</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">G</font></span><br/>

<span class="kw">thus </span> <a href="isocat_2.html#K10" title="ISOCAT_2:func.10">Pr2</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span> = 
<span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">&lt;:</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font></span><a href="isocat_2.html#K8" title="ISOCAT_2:func.8">:&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#D11" title="CAT_2:def.11">CAT_2:def 11</a></span>
<br/>.= 
<font color="Maroon" title="c5">G</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T82" title="FUNCT_3:th.82">FUNCT_3:82</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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