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<span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">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">  ex <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font> st <br/>( <font color="Olive" title="b2">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Olive" title="b1">F</font>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <font color="Olive" title="b1">F</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Olive" title="b2">G</font>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<span class="kw">take </span>
 <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</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">  ex <font color="Olive" title="b1">G</font> being   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c3">A</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Olive" title="b1">G</font>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<span class="kw">take </span>
 <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</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"> ( <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:18_1_1"/>
( <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  &amp; <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font></span>)</span>, <a href="functor0.html#K11" title="FUNCTOR0:func.11">id</a> <font color="Maroon" title="c3">A</font> <a href="functor3.html#R1" title="FUNCTOR3:pred.1">are_naturally_equivalent</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="functor3.html#T4" onmouseover="rs('functor3/T4')" onmouseout="rh()">FUNCTOR3:4</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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