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<b>let </b><font color="Maroon" title="c1">SAS</font> be   <a href="semi_af1.html#NM1" title="SEMI_AF1:NM.1">Semi_Affine_Space</a>;<br/><b>let </b><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">SAS</font>;<br/>









<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E61">A1</font></i>: 
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</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>
 ;<br/>

<div><i><font color="Green" title="E62">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ;<br/><a NAME="E2:71_1"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="semi_af1.html#T73" target="_self" title="SEMI_AF1:th.73">Th73</a></i>;<br/><b>hence </b><a NAME="E3:71_1"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T84" target="_self" title="SEMI_AF1:th.84">Th84</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E63">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/><a NAME="E2:71_2"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> &amp;  <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="semi_af1.html#T84" target="_self" title="SEMI_AF1:th.84">Th84</a></i>;<br/><a NAME="E3:71_2"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T81" target="_self" title="SEMI_AF1:th.81">Th81</a></i>;<br/><b>hence </b><a NAME="E4:71_2"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D4" target="_self" title="SEMI_AF1:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E64">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_3"/><i><font color="Green" title="E65">A5</font></i>: 
( <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> &amp; <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> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )
 ;<br/><b>then consider </b><font color="Maroon" title="c6">p</font>, <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">SAS</font><b> such that </b><br/><a NAME="E3:71_3"/><i><font color="Green" title="E66">A6</font></i>: 
(  <a href="semi_af1.html#R2" title="SEMI_AF1: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> &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1: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> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="semi_af1.html#D4" target="_self" title="SEMI_AF1:def.4">Def4</a></i>;<br/><a NAME="E4:71_3"/>
( not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">p</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">p</font> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="semi_af1.html#E3:71_3"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a>, <a class="ref" href="semi_af1.html#T12" target="_self" title="SEMI_AF1:th.12">Th12</a>, <a class="ref" href="semi_af1.html#T54" target="_self" title="SEMI_AF1:th.54">Th54</a>, <a class="ref" href="semi_af1.html#T56" target="_self" title="SEMI_AF1:th.56">Th56</a></i>;<br/><a NAME="E5:71_3"/><b>then </b>
not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">p</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="semi_af1.html#T39" target="_self" title="SEMI_AF1:th.39">Th39</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font><b> such that </b><br/><a NAME="E7:71_3"/><i><font color="Green" title="E67">A7</font></i>: 
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T62" target="_self" title="SEMI_AF1:th.62">Th62</a></i>;<br/><a NAME="E8:71_3"/><i><font color="Green" title="E68">A8</font></i>: 
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E7:71_3"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="semi_af1.html#T61" target="_self" title="SEMI_AF1:th.61">Th61</a></i>;<br/><a NAME="E9:71_3"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="semi_af1.html#T37" target="_self" title="SEMI_AF1:th.37">Th37</a></i>;<br/><a NAME="E10:71_3"/><b>then </b><i><font color="Green" title="E69">A9</font></i>: 
not <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c3">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="semi_af1.html#E7:71_3"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="semi_af1.html#T57" target="_self" title="SEMI_AF1:th.57">Th57</a></i>;<br/><a NAME="E11:71_3"/>
( <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> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E3:71_3"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a>, <a class="ref" href="semi_af1.html#T54" target="_self" title="SEMI_AF1:th.54">Th54</a></i>;<br/><a NAME="E12:71_3"/><b>then </b><i><font color="Green" title="E70">A10</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/><a NAME="E13:71_3"/><b>then </b>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font> &amp; <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> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="semi_af1.html#E7:71_3"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a>, <a class="ref" href="semi_af1.html#T49" target="_self" title="SEMI_AF1:th.49">Th49</a></i>;<br/><a NAME="E14:71_3"/><b>then </b><i><font color="Green" title="E71">A11</font></i>: 
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/><a NAME="E15:71_3"/>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E3:71_3"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a></i>;<br/><a NAME="E16:71_3"/><b>then </b>
( <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> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="ref" href="semi_af1.html#D2" target="_self" title="SEMI_AF1:def.2">Def2</a>, <a class="ref" href="semi_af1.html#T17" target="_self" title="SEMI_AF1:th.17">Th17</a></i>;<br/><a NAME="E17:71_3"/><b>then </b>
( <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> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="semi_af1.html#E7:71_3"><i><font color="Green" title="E67">A7</font></i></a>, <a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a></i>;<br/><a NAME="E18:71_3"/><b>then </b>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/><a NAME="E19:71_3"/><b>then </b><i><font color="Green" title="E72">A12</font></i>: 
<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c6">p</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T18" target="_self" title="SEMI_AF1:th.18">Th18</a></i>;<br/><a NAME="E20:71_3"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71_3"><i><font color="Green" title="E65">A5</font></i></a>, <a class="txt" href="semi_af1.html#E12:71_3"><i><font color="Green" title="E70">A10</font></i></a>, <a class="ref" href="semi_af1.html#T50" target="_self" title="SEMI_AF1:th.50">Th50</a></i>;<br/><a NAME="E21:71_3"/><b>then </b><i><font color="Green" title="E73">A13</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T18" target="_self" title="SEMI_AF1:th.18">Th18</a></i>;<br/><a NAME="E22:71_3"/>
( <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E3:71_3"><i><font color="Green" title="E66">A6</font></i></a>, <a class="txt" href="semi_af1.html#E8:71_3"><i><font color="Green" title="E68">A8</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a>, <a class="ref" href="semi_af1.html#T54" target="_self" title="SEMI_AF1:th.54">Th54</a></i>;<br/><a NAME="E23:71_3"/><b>then </b><i><font color="Green" title="E74">A14</font></i>: 
<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/><a NAME="E24:71_3"/>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E3:71_3"><i><font color="Green" title="E66">A6</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a></i>;<br/><a NAME="E25:71_3"/><b>then </b>
<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T17" target="_self" title="SEMI_AF1:th.17">Th17</a></i>;<br/><a NAME="E26:71_3"/><b>then </b>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E19:71_3"><i><font color="Green" title="E72">A12</font></i></a>, <a class="txt" href="semi_af1.html#E21:71_3"><i><font color="Green" title="E73">A13</font></i></a>, <a class="txt" href="semi_af1.html#E23:71_3"><i><font color="Green" title="E74">A14</font></i></a>, <a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">Def1</a></i>;<br/><a NAME="E27:71_3"/><b>then </b>
(  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="txt" href="semi_af1.html#E7:71_3"><i><font color="Green" title="E67">A7</font></i></a>, <a class="txt" href="semi_af1.html#E10:71_3"><i><font color="Green" title="E69">A9</font></i></a>, <a class="txt" href="semi_af1.html#E14:71_3"><i><font color="Green" title="E71">A11</font></i></a>, <a class="ref" href="semi_af1.html#D3" target="_self" title="SEMI_AF1:def.3">Def3</a>, <a class="ref" href="semi_af1.html#T61" target="_self" title="SEMI_AF1:th.61">Th61</a></i>;<br/><b>hence </b><a NAME="E28:71_3"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D4" target="_self" title="SEMI_AF1:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:71_4"/>
( <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> &amp; <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> &amp; not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a>  )
 ;<br/><a NAME="E2:71_4"/><b>then </b>
 <a href="semi_af1.html#R2" title="SEMI_AF1: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>
 <b>by </b><i><a class="txt" href="semi_af1.html#E1:71"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="semi_af1.html#T78" target="_self" title="SEMI_AF1:th.78">Th78</a></i>;<br/><a NAME="E3:71_4"/><b>then </b>
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T61" target="_self" title="SEMI_AF1:th.61">Th61</a></i>;<br/><b>hence </b><a NAME="E4:71_4"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T79" target="_self" title="SEMI_AF1:th.79">Th79</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:71"/>
 <a href="semi_af1.html#R3" title="SEMI_AF1:pred.3">congr</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="semi_af1.html#E2:71"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="semi_af1.html#E3:71"><i><font color="Green" title="E63">A3</font></i></a>, <a class="txt" href="semi_af1.html#E4:71"><i><font color="Green" title="E64">A4</font></i></a></i>;<br/>


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