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<span class="kw">let </span><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:()"><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">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</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">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_2.html#R3" title="PARSP_2:pred.3">congr</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> implies <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R3" title="PARSP_2:pred.3">congr</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> )</span><br/>









<a NAME="E1:77"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_1.html#T42" title="PARSP_1:th.42">PARSP_1:42</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:77"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
 <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">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R3" title="PARSP_2:pred.3">congr</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><br/>

<a NAME="E3:77"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A3</font></span>: 
( not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#T34" target="_self" title="PARSP_2:th.34">Th34</a>, <a class="ref" href="parsp_2.html#T36" target="_self" title="PARSP_2:th.36">Th36</a></span>;<br/>
<a NAME="E4:77"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="parsp_2.html#T34" target="_self" title="PARSP_2:th.34">Th34</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><span class="kw"> such that </span><br/><a NAME="E6:77"/><span class="lab"><font color="Green" title="E58">A4</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">p</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E7:77"/><span class="lab"><font color="Green" title="E59">A5</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p</font>
 <span class="kw">and </span><br/><a NAME="E8:77"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<font color="Maroon" title="c4">c</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="ref" href="parsp_2.html#T46" target="_self" title="PARSP_2:th.46">Th46</a></span>;<br/>
<a NAME="E9:77"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</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">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:77"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><span class="kw"> such that </span><br/><a NAME="E11:77"/><span class="lab"><font color="Green" title="E61">A7</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:77"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="txt" href="#E3:77"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="ref" href="parsp_2.html#T17" target="_self" title="PARSP_2:th.17">Th17</a>, <a class="ref" href="parsp_2.html#T42" target="_self" title="PARSP_2:th.42">Th42</a></span>;<br/>
<a NAME="E12:77"/>
 <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">b</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:77"><span class="lab"><font color="Green" title="E61">A7</font></span></a>, <a class="ref" href="parsp_2.html#T41" target="_self" title="PARSP_2:th.41">Th41</a></span>;<br/>
<a NAME="E13:77"/><span class="kw">then </span>
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="txt" href="#E6:77"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="txt" href="#E8:77"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="ref" href="parsp_2.html#T49" target="_self" title="PARSP_2:th.49">Th49</a></span>;<br/>
<a NAME="E14:77"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A8</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#T41" target="_self" title="PARSP_2:th.41">Th41</a></span>;<br/>
<a NAME="E15:77"/>
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:77"><span class="lab"><font color="Green" title="E61">A7</font></span></a>, <a class="ref" href="parsp_2.html#T41" target="_self" title="PARSP_2:th.41">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:77"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R3" title="PARSP_2:pred.3">congr</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:77"><span class="lab"><font color="Green" title="E62">A8</font></span></a>, <a class="ref" href="parsp_2.html#D4" target="_self" title="PARSP_2:def.4">Def4</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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