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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">I</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">C</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">D</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Olive" title="b1">B</font>  st <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">D</font> holds <br/>for <font color="Olive" title="b4">F</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Olive" title="b4">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b1">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b3">D</font></span><br/><b>let </b><font color="Maroon" title="c3">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">D</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c3">B</font>  st <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">D</font> holds <br/>for <font color="Olive" title="b3">F</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Olive" title="b3">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b2">D</font></span><br/><b>let </b><font color="Maroon" title="c4">C</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c3">B</font>  st <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D</font> holds <br/>for <font color="Olive" title="b2">F</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Olive" title="b2">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Olive" title="b1">D</font></span><br/><b>let </b><font color="Maroon" title="c5">D</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_2.html#M1" title="ALTCAT_2:mode.1">SubCatStr</a> of <font color="Maroon" title="c3">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font> implies for <font color="Olive" title="b1">F</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Olive" title="b1">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c5">D</font> )</span><br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Olive" title="b1">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c5">D</font></span><br/>

<b>let </b><font color="Maroon" title="c6">F</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c5">D</font></span><br/>

<b>thus </b><font color="Maroon" title="c6">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c4">C</font> = 
<font color="Maroon" title="c6">F</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p2">(<span class="default"><a href="functor0.html#K10" title="FUNCTOR0:func.10">incl</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor1.html#T5" target="_self" title="FUNCTOR1:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="functor0.html#K14" title="FUNCTOR0:func.14">|</a> <font color="Maroon" title="c5">D</font>
<b>by </b><i><a class="ref" href="functor0.html#T33" title="FUNCTOR0:th.33">FUNCTOR0:33</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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