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<span class="kw">let </span><font color="Maroon" title="c1">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#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> holds  <span class="p1">(<span class="default"><a href="oppcat_1.html#K11" title="OPPCAT_1:func.11">*id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="oppcat_1.html#K11" title="OPPCAT_1:func.11">*id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c2">f</font></span><br/>



<span class="kw">thus </span><span class="p1">(<span class="default"><a href="oppcat_1.html#K11" title="OPPCAT_1:func.11">*id</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">f</font> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K11" title="CAT_1:func.11">id</a> <font color="Maroon" title="c1">C</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="c2">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/>.= 
 <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</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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