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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">S</font>, <font color="Olive" title="b2">T</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> holds   <a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Olive" title="b1">S</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">T</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">T</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/>



<b>consider </b><font color="Maroon" title="c4">F</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c2">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">T</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E2:61"/><i><font color="Green" title="E46">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="waybel27.html#V3" title="WAYBEL27:attr.3">commuting</a> &amp; <font color="Maroon" title="c4">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> )
 <b>by </b><i><a class="ref" href="waybel27.html#T41" target="_self" title="WAYBEL27:th.41">Th41</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">F</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a></span><br/>

<b>thus </b><a NAME="E3:61"/>
<font color="Maroon" title="c4">F</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="waybel27.html#E2:61"><i><font color="Green" title="E46">A1</font></i></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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