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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" 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> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">A</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  holds <br/> ex <font color="Olive" title="b3">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">K</font> &amp; <font color="Olive" title="b1">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b3">K</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" 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> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">A</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  holds <br/> ex <font color="Olive" title="b2">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">K</font> &amp; <font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b2">K</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  implies  ex <font color="Olive" title="b1">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b1">K</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:4"/>
<font color="Maroon" title="c2">A</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b1">K</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:4"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E4:4"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D12" title="ANALMETR:def.12">ANALMETR:def 12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E6:4"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E7:4"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c8">d9</font> = <font color="Maroon" title="c6">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c9">K</font> =  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">K</font> &amp; <font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">K</font> )</span><br/>

<a NAME="E9:4"/>
<font color="Maroon" title="c9">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">d9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T41" title="ANALMETR:th.41">ANALMETR:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:4"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">K</font></span><br/>

<span class="kw">thus </span><a NAME="E11:4"/>
<font color="Maroon" title="c2">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E6:4"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="analmetr.html#T45" title="ANALMETR:th.45">ANALMETR:45</a></span>; <a class="txt" 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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