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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</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">a</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b5">P</font>, <font color="Olive" title="b6">Q</font>, <font color="Olive" title="b7">R</font>, <font color="Olive" title="b8">A</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <font color="Olive" title="b1">a</font> <a href="projpl_1.html#R3" title="PROJPL_1:pred.3">on</a> <font color="Olive" title="b5">P</font>,<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b7">R</font> &amp; <font color="Olive" title="b5">P</font>,<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b7">R</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Olive" title="b1">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b2">p</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b8">A</font>,<font color="Olive" title="b5">P</font> &amp; <font color="Olive" title="b3">q</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b8">A</font>,<font color="Olive" title="b6">Q</font> &amp; <font color="Olive" title="b4">r</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b8">A</font>,<font color="Olive" title="b7">R</font> holds <br/><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">r</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</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">P</font>, <font color="Olive" title="b2">Q</font>, <font color="Olive" title="b3">R</font>, <font color="Olive" title="b4">A</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#R3" title="PROJPL_1:pred.3">on</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font>,<font color="Olive" title="b3">R</font> &amp; <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font>,<font color="Olive" title="b3">R</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Olive" title="b4">A</font> &amp; <font color="Maroon" title="c3">p</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b4">A</font>,<font color="Olive" title="b1">P</font> &amp; <font color="Maroon" title="c4">q</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b4">A</font>,<font color="Olive" title="b2">Q</font> &amp; <font color="Maroon" title="c5">r</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Olive" title="b4">A</font>,<font color="Olive" title="b3">R</font> holds <br/><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">r</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">P</font>, <font color="Maroon" title="c7">Q</font>, <font color="Maroon" title="c8">R</font>, <font color="Maroon" title="c9">A</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</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="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#R3" title="PROJPL_1:pred.3">on</a> <font color="Maroon" title="c6">P</font>,<font color="Maroon" title="c7">Q</font>,<font color="Maroon" title="c8">R</font> &amp; <font color="Maroon" title="c6">P</font>,<font color="Maroon" title="c7">Q</font>,<font color="Maroon" title="c8">R</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c3">p</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c4">q</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c7">Q</font> &amp; <font color="Maroon" title="c5">r</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c8">R</font> implies <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">r</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  )</span><br/>

















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:30"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is  <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a> 
 <span class="kw">and </span><br/><a NAME="E2:30"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="projpl_1.html#R3" title="PROJPL_1:pred.3">on</a> <font color="Maroon" title="c6">P</font>,<font color="Maroon" title="c7">Q</font>,<font color="Maroon" title="c8">R</font>
 <span class="kw">and </span><br/><a NAME="E3:30"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c6">P</font>,<font color="Maroon" title="c7">Q</font>,<font color="Maroon" title="c8">R</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> 
 <span class="kw">and </span><br/><a NAME="E4:30"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c9">A</font>
 <span class="kw">and </span><br/><a NAME="E5:30"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c6">P</font>
 <span class="kw">and </span><br/><a NAME="E6:30"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c7">Q</font>
 <span class="kw">and </span><br/><a NAME="E7:30"/><span class="lab"><font color="Green" title="E33">A7</font></span>: 
<font color="Maroon" title="c5">r</font> <a href="projpl_1.html#R2" title="PROJPL_1:pred.2">on</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c8">R</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">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">r</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> </span><br/>

<a NAME="E8:30"/><span class="lab"><font color="Green" title="E34">A8</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">R</font> &amp; <font color="Maroon" title="c5">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E7:30"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="projpl_1.html#D2" target="_self" title="PROJPL_1:def.2">Def2</a>, <a class="ref" href="projpl_1.html#D3" target="_self" title="PROJPL_1:def.3">Def3</a></span>;<br/>
<a NAME="E9:30"/><span class="lab"><font color="Green" title="E35">A9</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="projpl_1.html#D2" target="_self" title="PROJPL_1:def.2">Def2</a>, <a class="ref" href="projpl_1.html#D3" target="_self" title="PROJPL_1:def.3">Def3</a></span>;<br/>
<a NAME="E10:30"/>
( <font color="Maroon" title="c7">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">R</font> &amp; <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E6:30"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="projpl_1.html#D2" target="_self" title="PROJPL_1:def.2">Def2</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E11:30"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A10</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E9:30"><span class="lab"><font color="Green" title="E35">A9</font></span></a>, <a class="txt" href="#E8:30"><span class="lab"><font color="Green" title="E34">A8</font></span></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></span>;<br/>
<a NAME="E12:30"/><span class="lab"><font color="Green" title="E37">A11</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:30"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="projpl_1.html#D2" target="_self" title="PROJPL_1:def.2">Def2</a></span>;<br/>
<a NAME="E13:30"/><span class="lab"><font color="Green" title="E38">A12</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c3">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E5:30"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="projpl_1.html#D2" target="_self" title="PROJPL_1:def.2">Def2</a>, <a class="ref" href="projpl_1.html#D3" target="_self" title="PROJPL_1:def.3">Def3</a></span>;<br/>
<a NAME="E14:30"/>
<font color="Maroon" title="c8">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E15:30"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A13</font></span>: 
<font color="Maroon" title="c5">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E13:30"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E12:30"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="txt" href="#E8:30"><span class="lab"><font color="Green" title="E34">A8</font></span></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></span>;<br/>
<a NAME="E16:30"/>
<font color="Maroon" title="c6">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E17:30"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E13:30"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E12:30"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="txt" href="#E9:30"><span class="lab"><font color="Green" title="E35">A9</font></span></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:30"/>
<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">r</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:30"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="txt" href="#E15:30"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</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/>


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