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<b>let </b><font color="Maroon" title="c1">FdSp</font> be   <a href="parsp_2.html#NM1" title="PARSP_2:NM.1">FanodesSp</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">a</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font>  st  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">q</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">r</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b4">q</font>,<font color="Olive" title="b6">r</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">q</font>, <font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">r</font> implies <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">r</font> )</span><br/>













<b>assume </b><a NAME="E1:54"/>
(  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">r</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">r</font></span><br/>

<a NAME="E2:54"/><b>then </b>
( not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">r</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c7">r</font> )
 
<b>by </b><i><a class="ref" href="parsp_2.html#D3" target="_self" title="PARSP_2:def.3">Def3</a></i>;<br/>
<a NAME="E3:54"/><b>then </b>
( not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">r</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c7">r</font> )
 
<b>by </b><i><a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="ref" href="parsp_2.html#D1" target="_self" title="PARSP_2:def.1">Def1</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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