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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:129"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V23" target="_self">isomorphic</a>
 ;<br/>

<a NAME="E2:129"/><b>then </b><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#D38" target="_self">Def38</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:129"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a>  &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E1:129"><i><font color="Green">E57</font></i></a>, <a class="ref" href="waybel_0.html#D38" target="_self">Def38</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E5:129"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</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">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> &amp; not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> ) or <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><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">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> &amp; not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/><div class="add"><b>thus </b><a NAME="E2:129_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green">E58</font></i></a>, <a class="txt" href="waybel_0.html#E4:129"><i><font color="Green">E59</font></i></a>, <a class="txt" href="waybel_0.html#E5:129"><i><font color="Green">E60</font></i></a>, <a class="ref" href="funct_1.html#T62">FUNCT_1:62</a></i>;<br/><a NAME="E3:129_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green">E58</font></i></a>, <a class="ref" href="funct_1.html#T65">FUNCT_1:65</a></i>;<br/><b>hence </b><a NAME="E4:129_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K2">"</a>  &amp; <font color="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E2:129"><i><font color="Green">E58</font></i></a>, <a class="txt" href="waybel_0.html#E5:129"><i><font color="Green">E60</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">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:129_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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