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<span class="kw">let </span><font color="Maroon" title="c5">CLSP</font> be   <a href="collsp.html#NM2" title="COLLSP:NM.2">CollSp</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">r</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">CLSP</font>  st <font color="Olive" title="b3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">p</font>, <font color="Maroon" title="c9">q</font>, <font color="Maroon" title="c10">r</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">CLSP</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  implies <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:15"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c8">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font>
 <span class="kw">and </span><br/><a NAME="E2:15"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  )
 <span class="kw">and </span><br/><a NAME="E3:15"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> implies <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a>  )</span></a><div class="add"><span class="kw">assume </span><a NAME="E1:15_1"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> </span><br/><a NAME="E2:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="collsp.html#T6" target="_self" onmouseover="rs('collsp/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E3:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A5</font></span>: 
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c6">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="collsp.html#T8" target="_self" onmouseover="rs('collsp/T8')" onmouseout="rh()">Th8</a></span>;<br/><a NAME="E4:15_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c7">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="collsp.html#T2" target="_self" onmouseover="rs('collsp/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E5:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c7">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="collsp.html#T3" target="_self" onmouseover="rs('collsp/T3')" onmouseout="rh()">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E6:15_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="collsp.html#T3" target="_self" onmouseover="rs('collsp/T3')" onmouseout="rh()">Th3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:15"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="collsp.html#T2" target="_self" onmouseover="rs('collsp/T2')" onmouseout="rh()">Th2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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