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<span class="kw">let </span><font color="Maroon" title="c1">AS</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="analoaf.html#L1" title="ANALOAF:struct.1">AffinStruct</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">S</font> being   <a href="analoaf.html#NM2" title="ANALOAF:NM.2">OAffinPlane</a>  st <font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Olive" title="b1">S</font> holds <br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font>, <font color="Olive" title="b5">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st  not <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">z</font>,<font color="Olive" title="b5">t</font> holds <br/> ex <font color="Olive" title="b6">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b6">u</font> &amp; <font color="Olive" title="b4">z</font>,<font color="Olive" title="b5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">z</font>,<font color="Olive" title="b6">u</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="analoaf.html#NM2" title="ANALOAF:NM.2">OAffinPlane</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="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">S</font> implies  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st  not <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> holds <br/> ex <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b5">u</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:45"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c1">AS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c2">S</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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st  not <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> holds <br/> ex <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b5">u</font> &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b5">u</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font>, <font color="Maroon" title="c6">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</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"> (  not <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</font> implies  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Olive" title="b1">u</font> ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">x9</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c8">y9</font> = <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c9">z9</font> = <font color="Maroon" title="c5">z</font>, <font color="Maroon" title="c10">t9</font> = <font color="Maroon" title="c6">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E33">A1</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:45"/>
 not <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</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">  ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Olive" title="b1">u</font> )</span><br/>

<a NAME="E4:45"/><span class="kw">then </span>
 not <font color="Maroon" title="c7">x9</font>,<font color="Maroon" title="c8">y9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c9">z9</font>,<font color="Maroon" title="c10">t9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="diraf.html#T38" target="_self" onmouseover="rs('diraf/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">u9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E6:45"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
( <font color="Maroon" title="c7">x9</font>,<font color="Maroon" title="c8">y9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c7">x9</font>,<font color="Maroon" title="c11">u9</font> &amp; <font color="Maroon" title="c9">z9</font>,<font color="Maroon" title="c10">t9</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c9">z9</font>,<font color="Maroon" title="c11">u9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T43" target="_self" onmouseover="rs('diraf/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">u</font> = <font color="Maroon" title="c11">u9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E33">A1</font></span></a></span>;<br/>
<a NAME="E8:45"/>
( <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c12">u</font> &amp; <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c12">u</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E6:45"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="diraf.html#T38" target="_self" onmouseover="rs('diraf/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:45"/>
 ex <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">z</font>,<font color="Olive" title="b1">u</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"> verum</span><br/>


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