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<span class="kw">let </span><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</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">OAS</font>  holds <br/>(  not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> or <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> or  ex <font color="Olive" title="b5">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">x</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">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> or  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:75"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <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="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> or  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:75"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</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">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E36">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c6">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E2:75_1"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">and </span><br/><a NAME="E3:75_1"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><span class="kw">assume </span><a NAME="E4:75_1"/><span class="lab"><font color="Green" title="E39">A6</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="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )</span><br/><div><span class="lab"><font color="Green" title="E40">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:75_1_1"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E4:75_1"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E2:75_1"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/><a NAME="E2:75_1_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E3:75_1_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E4:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E5:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">d</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E7:75_1_1"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">and </span><br/><a NAME="E8:75_1_1"/><span class="lab"><font color="Green" title="E42">A9</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:75_1"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><span class="kw">assume </span><a NAME="E9:75_1_1"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E10:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75_1"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E8:75_1_1"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/><a NAME="E11:75_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><a NAME="E12:75_1_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E13:75_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A10</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E14:75_1_1"/>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:75_1_1"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><a NAME="E15:75_1_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E16:75_1_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><span class="kw">hence </span><a NAME="E17:75_1_1"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:75_1_1"><span class="lab"><font color="Green" title="E43">A10</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:75_1_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E2:75_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:75_1"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><a NAME="E3:75_1_2"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E4:75_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A11</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E5:75_1_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><span class="kw">hence </span><a NAME="E6:75_1_2"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:75_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:75_1"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:75_1"><span class="lab"><font color="Green" title="E40">A7</font></span></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/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:75_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E2:75_2"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><span class="kw">hence </span><a NAME="E3:75_2"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:75"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:75"><span class="lab"><font color="Green" title="E36">A3</font></span></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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