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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="hilbert3.html#NM1">SetValuation</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hilbert3.html#M1" target="_self">Permutation</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><a NAME="E1:46"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a>  <a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a>  <a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:46"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</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> <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="funct_3.html#K16">:]</a></span> &amp; <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="hilbert3.html#K1" target="_self">=&gt;</a> <font color="Olive">b<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="hilbert3.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:46"/>
 <a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="hilbert3.html#K1" target="_self">=&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="hilbert3.html#E1:46"><i><font color="Green">E37</font></i></a></i>;<br/>


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