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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E28">A1</font></i>: 
 ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>for <font color="Olive" title="b3">w</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">b</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">*</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">w</font>
 ;<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>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span>;<br/>

<b>set </b><font color="Maroon" title="c6">S</font> =  <a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font>;<br/>
<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E29">A2</font></i>: 
( not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> &amp; not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="analoaf.html#D2" target="_self" title="ANALOAF:def.2">ANALOAF:def 2</a><br/>

<b>reconsider </b><font color="Maroon" title="c7">a'</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c8">b'</font> = <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c9">c'</font> = <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c10">d'</font> = <font color="Maroon" title="c5">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E4:31"/>
( not <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c10">d'</font> &amp; not <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">d'</font>,<font color="Maroon" title="c9">c'</font> )
 
<b>by </b><i><a class="txt" href="analoaf.html#E2:31"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="analoaf.html#T33" target="_self" title="ANALOAF:th.33">Th33</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">t'</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E6:31"/><i><font color="Green" title="E30">A3</font></i>: 
( ( <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c11">t'</font> or <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">t'</font>,<font color="Maroon" title="c7">a'</font> ) &amp; ( <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c10">d'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c11">t'</font> or <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c10">d'</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c11">t'</font>,<font color="Maroon" title="c9">c'</font> ) )
 <b>by </b><i><a class="txt" href="analoaf.html#E1:31"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="analoaf.html#T31" target="_self" title="ANALOAF:th.31">Th31</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">t</font> = <font color="Maroon" title="c11">t'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> ;<br/>
<a NAME="E8:31"/>
( ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> ) &amp; ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="analoaf.html#E6:31"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="analoaf.html#T33" target="_self" title="ANALOAF:th.33">Th33</a></i>;<br/>
<a NAME="E9:31"/><b>then </b>
( ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">t</font> or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">t</font> or <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">t</font>,<font color="Maroon" title="c4">c</font> ) )
 
<b>by </b><i><a class="ref" href="analoaf.html#D2" target="_self" title="ANALOAF:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E10:31"/>
 ex <font color="Olive" title="b1">t</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analoaf.html#K2" title="ANALOAF:func.2">OASpace</a> <font color="Maroon" title="c1">V</font></span>)</span> st <br/>( ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">t</font> or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">t</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Olive" title="b1">t</font> or <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">t</font>,<font color="Maroon" title="c4">c</font> ) )
 ;<br/>


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