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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><br/> for <font color="Olive" title="b4">a'</font>, <font color="Olive" title="b5">b'</font>, <font color="Olive" title="b6">c'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a'</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">b'</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">c'</font> holds <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b4">a'</font>,<font color="Olive" title="b5">b'</font>,<font color="Olive" title="b6">c'</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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:()"><i><font color="Red">::  thesis: </font></i></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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span>  st <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a'</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b'</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c'</font> holds <br/>(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">a'</font>,<font color="Olive" title="b2">b'</font>,<font color="Olive" title="b3">c'</font> )</span><br/><b>let </b><font color="Maroon" title="c5">a'</font>, <font color="Maroon" title="c6">b'</font>, <font color="Maroon" title="c7">c'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> implies (  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font> ) )</span><br/>





<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font> )</span><br/>

<div><i><font color="Green" title="E4">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:4_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><br/><a NAME="E2:4_1"/><b>then </b>
<font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E3:4_1"/><b>then </b>
<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="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></i>;<br/><b>hence </b><a NAME="E4:4_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:4_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font></span><br/><a NAME="E2:4_2"/><b>then </b>
<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="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E3:4_2"/><b>then </b>
<font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="diraf.html#T45" title="DIRAF:th.45">DIRAF:45</a></i>;<br/><b>hence </b><a NAME="E4:4_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:4"/>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> iff  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font> )
 <b>by </b><i><a class="txt" href="#E2:4"><i><font color="Green" title="E4">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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