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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#L1" target="_self">ShefferStr</a> ;<br/>

<b>assume </b><a NAME="E1:45_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>thus </b><a NAME="E2:45_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="sheffer1.html#V10" target="_self">satisfying_Sheffer_1</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="sheffer1.html#D13" target="_self">SHEFFER1:def 13</a><br/>

<b>thus </b><a NAME="E1:45_1_1_1"/>
<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="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>2</sub></font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:45_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:45_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="sheffer1.html#V11" target="_self">satisfying_Sheffer_2</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_2"><b>proof </b></a><div class="add">

<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>; <i><font color="Red">:: according to </font></i><a class="ref" href="sheffer1.html#D14" target="_self">SHEFFER1:def 14</a><br/>

<b>thus </b><a NAME="E1:45_1_1_2"/>
<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>3</sub></font> <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> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:45_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="sheffer1.html#D15" target="_self">SHEFFER1:def 15</a><br/>

<b>thus </b><a NAME="E4:45_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <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> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></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>4</sub></font> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="sheffer1.html#K5" target="_self">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:45_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


</div>
