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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> holds <br/><font color="Olive" title="b1">G</font> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a></span><br/><b>let </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">F</font> &amp; <font color="Maroon" title="c3">F</font> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> implies <font color="Maroon" title="c2">G</font> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:23"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c2">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">F</font>
 <b>and </b><br/><a NAME="E2:23"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G</font> is <a href="incsp_1.html#V3" title="INCSP_1:attr.3">linear</a></span><br/>

<b>consider </b><font color="Maroon" title="c4">L</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E4:23"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c4">L</font>
 <b>by </b><i><a class="txt" href="#E2:23"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">L</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">INCSP_1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G</font> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c4">L</font></span><br/>

<b>let </b><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>; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D4" target="_self" title="INCSP_1:def.4">INCSP_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c2">G</font> implies <font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">L</font> )</span><br/>

<b>assume </b><a NAME="E5:23"/>
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">L</font></span><br/>

<b>hence </b><a NAME="E6:23"/>
<font color="Maroon" title="c5">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">L</font>
 <b>by </b><i><a class="txt" href="#E1:23"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="#E4:23"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="incsp_1.html#D4" target="_self" title="INCSP_1:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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