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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">D</font> holds   <a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Olive" title="b1">S</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">S</font></span><br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>; <a class="txt" 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="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font> = 
<span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#D8" target="_self" title="OPPCAT_1:def.8">Def8</a></span>
<br/>.= 
<font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#D6" target="_self" title="OPPCAT_1:def.6">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font>

; <a class="txt" 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="E2:59"/>
 <a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>; <a class="txt" 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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