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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">p</font> holds <br/> 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/>( <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">x</font> &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">x</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">a</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font> implies  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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E2:24"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/>

<a NAME="E3:24"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E16">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E2:24_1"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><span class="kw">consider </span><font color="Maroon" title="c6">e1</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="E4:24_1"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">e1</font>
 <span class="kw">and </span><br/><a NAME="E5:24_1"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></span>;<br/><a NAME="E6:24_1"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">e2</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="E8:24_1"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">e2</font>
 <span class="kw">and </span><br/><a NAME="E9:24_1"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c7">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E10:24_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/><a NAME="E11:24_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><div><span class="lab"><font color="Green" title="E23">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E24">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E25">A13</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:24_1_1_1_1"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</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">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )</span><br/><a NAME="E2:24_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:24"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:24_1_1_1_1"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a>, <a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</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/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:24_1_1_1"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E3:24_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E4:24_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> or <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_1_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E5:24_1_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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="diraf.html#T1" title="DIRAF:th.1">DIRAF:1</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E25">A15</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:24_1_1_2"/><span class="lab"><font color="Green" title="E26">A16</font></span>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</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">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font> )</span><br/><a NAME="E2:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E3:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E1:24_1_1_2"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E4:24_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:24_1_1_2"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:24"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a>, <a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</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/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e2</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E4:24_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E11:24_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E9:24_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E5:24_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><span class="kw">hence </span><a NAME="E6:24_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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E2:24_1_1"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E24">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E25">A18</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24_1_2_1"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">and </span><br/><a NAME="E2:24_1_2_1"/><span class="lab"><font color="Green" title="E26">A19</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">a</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">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )</span><br/><a NAME="E3:24_1_2_1"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_2_1"><span class="lab"><font color="Green" title="E26">A19</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:24_1_2_1"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a>, <a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E26">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24_1_2_2"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">and </span><br/><a NAME="E2:24_1_2_2"/><span class="lab"><font color="Green" title="E27">A21</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">a</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">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )</span><br/><a NAME="E3:24_1_2_2"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_2_2"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:24_1_2_2"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a>, <a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</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/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E27">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24_1_2_3"/><span class="lab"><font color="Green" title="E28">A23</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">and </span><br/><a NAME="E2:24_1_2_3"/><span class="lab"><font color="Green" title="E29">A24</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">c</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">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">a</font> )</span><br/><a NAME="E3:24_1_2_3"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E1:24_1_2_3"><span class="lab"><font color="Green" title="E28">A23</font></span></a>, <a class="txt" href="#E2:24_1_2_3"><span class="lab"><font color="Green" title="E29">A24</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:24_1_2_3"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T1" title="DIRAF:th.1">DIRAF:1</a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</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/></div><span class="kw">end;</span></div><a NAME="E4:24_1_2"/><span class="lab"><font color="Green" title="E28">A25</font></span>: 
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c4">c</font> implies ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:24_1_2"/><span class="lab"><font color="Green" title="E29">A26</font></span>: 
<font color="Maroon" title="c6">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:24_1_2"/><span class="lab"><font color="Green" title="E30">A27</font></span>: 
<font color="Maroon" title="c7">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E7:24_1_2"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:24_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E5:24_1_2"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E8:24_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:24_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E6:24_1_2"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E9:24_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A28</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E10:24_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E11:24_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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:24_1_2"><span class="lab"><font color="Green" title="E31">A28</font></span></a>, <a class="txt" href="#E4:24_1_2"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E2:24_1_2"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E3:24_1_2"><span class="lab"><font color="Green" title="E27">A22</font></span></a>, <a class="txt" href="#E1:24_1_2"><span class="lab"><font color="Green" title="E25">A18</font></span></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:24_1_3"/><span class="lab"><font color="Green" title="E25">A29</font></span>: 
<font color="Maroon" title="c6">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e2</font>
 <span class="kw">and </span><br/><a NAME="E2:24_1_3"/><span class="lab"><font color="Green" title="E26">A30</font></span>: 
<font color="Maroon" title="c7">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 ; <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">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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )</span><br/><a NAME="E3:24_1_3"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e2</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:24_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E4:24_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">e2</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x</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="E6:24_1_3"/><span class="lab"><font color="Green" title="E27">A31</font></span>: 
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">x</font>
 <span class="kw">and </span><br/><a NAME="E7:24_1_3"/><span class="lab"><font color="Green" title="E28">A32</font></span>: 
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c7">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_3"><span class="lab"><font color="Green" title="E26">A30</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E8:24_1_3"/><span class="lab"><font color="Green" title="E29">A33</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E11:24_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E6:24_1_3"><span class="lab"><font color="Green" title="E27">A31</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E9:24_1_3"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:24_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E1:24_1_3"><span class="lab"><font color="Green" title="E25">A29</font></span></a>, <a class="txt" href="#E7:24_1_3"><span class="lab"><font color="Green" title="E28">A32</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><span class="kw">hence </span><a NAME="E10:24_1_3"/>
 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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:24_1_3"><span class="lab"><font color="Green" title="E29">A33</font></span></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E15:24_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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:24_1"><span class="lab"><font color="Green" title="E24">A17</font></span></a>, <a class="txt" href="#E12:24_1"><span class="lab"><font color="Green" title="E23">A11</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E5:24"/><span class="lab"><font color="Green" title="E17">A34</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> implies ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</a></span>;<br/>
<a NAME="E6:24"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> implies ( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">a</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="diraf.html#T1" title="DIRAF:th.1">DIRAF:1</a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:24"/>
 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/>( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24"><span class="lab"><font color="Green" title="E17">A34</font></span></a>, <a class="txt" href="#E4:24"><span class="lab"><font color="Green" title="E16">A4</font></span></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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