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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="sheffer1.html#V9" target="_self">properly_defined</a> <a href="sheffer1.html#V10" target="_self">satisfying_Sheffer_1</a> <a href="sheffer1.html#V11" target="_self">satisfying_Sheffer_2</a> <a href="sheffer1.html#V12" target="_self">satisfying_Sheffer_3</a>  <a href="sheffer1.html#L3" target="_self">ShefferOrthoLattStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 
<b>by </b><i><a class="ref" href="sheffer1.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 
<b>by </b><i><a class="ref" href="sheffer1.html#T32" target="_self">Th32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 
<b>by </b><i><a class="ref" href="sheffer1.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span></span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span> <a href="sheffer1.html#K6" target="_self">"</a> 

<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K6" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#T31" target="_self">Th31</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

;<br/>
<b>hence </b><a NAME="E2:55"/>
<font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


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