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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>given </b><font color="Maroon">c<sub>3</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><b> such that </b><a NAME="E1:24"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a><br/>

<b>assume </b><a NAME="E2:24"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:24"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E5:24"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="yellow14.html#E2:24"><i><font color="Green">E9</font></i></a></i>;<br/>
<a NAME="E6:24"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow14.html#E1:24"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E7:24"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E8:24"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="txt" href="yellow14.html#E6:24"><i><font color="Green">E12</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
;<br/>

<a NAME="E9:24"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="yellow14.html#E1:24"><i><font color="Green">E8</font></i></a>, <a class="txt" href="yellow14.html#E4:24"><i><font color="Green">E10</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<b>hence </b><a NAME="E10:24"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="yellow14.html#E6:24"><i><font color="Green">E12</font></i></a>, <a class="txt" href="yellow14.html#E8:24"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E11:24"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E12:24"/>
ex <font color="Olive">b<sub>1</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> st <br/>( <font color="Olive">b<sub>1</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="Olive">b<sub>1</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 
<b>by </b><i><a class="txt" href="yellow14.html#E1:24"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<a NAME="E13:24"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow14.html#E8:24"><i><font color="Green">E13</font></i></a>, <a class="txt" href="yellow14.html#E11:24"><i><font color="Green">E14</font></i></a>, <a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a></i>;<br/>
<a NAME="E14:24"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="yellow14.html#E5:24"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E15:24"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="tops_2.html#K2">/"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="yellow14.html#E1:24"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<b>hence </b><a NAME="E16:24"/>
<font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="yellow14.html#E6:24"><i><font color="Green">E12</font></i></a>, <a class="txt" href="yellow14.html#E8:24"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>;<br/>


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