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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="incsp_1.html#L2" title="INCSP_1:struct.2">IncStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">G</font>, <font color="Olive" title="b3">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b2">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b3">F</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Olive" title="b1">P</font> holds <br/><font color="Olive" title="b2">G</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Olive" title="b1">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="incsp_1.html#NM3" title="INCSP_1:NM.3">PLANE</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">F</font> &amp; <font color="Olive" title="b2">F</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font> holds <br/><font color="Olive" title="b1">G</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font>, <font color="Maroon" title="c4">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c4">F</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font> implies <font color="Maroon" title="c3">G</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:18"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
( <font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c4">F</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">G</font> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a> <font color="Maroon" title="c2">P</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">A</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="incsp_1.html#D5" target="_self" title="INCSP_1:def.5">INCSP_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font> implies <font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c2">P</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:18"/>
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c2">P</font></span><br/>

<span class="kw">hence </span><a NAME="E3:18"/>
<font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a> <font color="Maroon" title="c2">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="incsp_1.html#D5" target="_self" title="INCSP_1:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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