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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="pencil_1.html#V6" target="_self">identifying_close_blocks</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:57"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E2:57"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="pencil_1.html#V1" target="_self">closed_under_lines</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D2" target="_self">PENCIL_1:def 2</a><br/>

<b>assume </b><a NAME="E1:57_1"/>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E2:57_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="pencil_1.html#E1:57"><i><font color="Green">E38</font></i></a>, <a class="ref" href="pencil_1.html#D7" target="_self">Def7</a></i>;<br/>


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


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