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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/>



<b>assume </b><a NAME="E1:129"/><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 ;<br/>

<a NAME="E2:129"/><b>then </b><i><font color="Green" title="E58">A2</font></i>: 
( <font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c3">f</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#D38" target="_self" title="WAYBEL_0:def.38">Def38</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">h</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E4:129"/><i><font color="Green" title="E59">A3</font></i>: 
( <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Maroon" title="c4">h</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E1:129"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="waybel_0.html#D38" target="_self" title="WAYBEL_0:def.38">Def38</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font>;<br/>

<b>assume </b><a NAME="E5:129"/><i><font color="Green" title="E60">A4</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:129_1"/>
( ( not <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> ) or <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 </span>;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D38" target="_self" title="WAYBEL_0:def.38">WAYBEL_0:def 38</a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_1_1"><b>case </b></a><a NAME="E1:129_1_1"/>
( not <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ;<br/><div class="add"><b>thus </b><a NAME="E2:129_1_1"/>
( <font color="Maroon" title="c5">g</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c5">g</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="waybel_0.html#E4:129"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="waybel_0.html#E5:129"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="funct_1.html#T62" title="FUNCT_1:th.62">FUNCT_1:62</a></i>;<br/><a NAME="E3:129_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="funct_1.html#T65" title="FUNCT_1:th.65">FUNCT_1:65</a></i>;<br/><b>hence </b><a NAME="E4:129_1_1"/>
 ex <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Olive" title="b1">g</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="waybel_0.html#E5:129"><i><font color="Green" title="E60">A4</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_1_2"><b>case </b></a><a NAME="E1:129_1_2"/>
( <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:129_1_2"/>
( <font color="Maroon" title="c2">T</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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