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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">l</font> being  <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">L</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">l</font> holds <br/><font color="Olive" title="b2">L</font> is  <a href="pencil_1.html#V1" title="PENCIL_1:attr.1">closed_under_lines</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">l</font> be   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> holds <br/><font color="Olive" title="b1">L</font> is  <a href="pencil_1.html#V1" title="PENCIL_1:attr.1">closed_under_lines</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> implies <font color="Maroon" title="c3">L</font> is  <a href="pencil_1.html#V1" title="PENCIL_1:attr.1">closed_under_lines</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:57"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">L</font> is  <a href="pencil_1.html#V1" title="PENCIL_1:attr.1">closed_under_lines</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:57"/>
<font color="Maroon" title="c3">L</font> is  <a href="pencil_1.html#V1" title="PENCIL_1:attr.1">closed_under_lines</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">K</font> be   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <font color="Maroon" title="c1">S</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pencil_1.html#D2" target="_self" title="PENCIL_1:def.2">PENCIL_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">L</font></span>)</span> implies <font color="Maroon" title="c4">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">L</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:57_1"/>
2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">L</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">L</font></span><br/>

<span class="kw">hence </span><a NAME="E2:57_1"/>
<font color="Maroon" title="c4">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="pencil_1.html#D7" target="_self" title="PENCIL_1:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>


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