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<a NAME="E1:56"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c1">D</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="flexary1.html#V1" title="FLEXARY1:attr.1">double-one-to-one</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  ;<br/>
<a NAME="E3:56"/>
 <a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <font color="Maroon" title="c1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c1">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_6.html#T23" onmouseover="rs('funct_6/T23')" onmouseout="rh()">FUNCT_6:23</a></span>;<br/>
<a NAME="E4:56"/><span class="kw">then </span>
 <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <font color="Maroon" title="c1">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_6.html#T26" onmouseover="rs('funct_6/T26')" onmouseout="rh()">FUNCT_6:26</a></span>;<br/>
<a NAME="E5:56"/><span class="kw">then </span>
 <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D9" onmouseover="rs('matrix_0/D9')" onmouseout="rh()">MATRIX_0:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:56"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D7" target="_self" onmouseover="rs('flexary1/D7')" onmouseout="rh()">Def7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> is    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E7:56"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">F</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<a NAME="E9:56"/>
( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">F</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  &amp;  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">F</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">F</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" onmouseover="rs('finseq_1/T38')" onmouseout="rh()">FINSEQ_1:38</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">FF</font> = <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">F</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> as   <a href="flexary1.html#V1" title="FLEXARY1:attr.1">double-one-to-one</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<a NAME="E11:56"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
 <a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <font color="Maroon" title="c3">FF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T132" onmouseover="rs('finseq_3/T132')" onmouseout="rh()">FINSEQ_3:132</a></span>;<br/>
<a NAME="E12:56"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" onmouseover="rs('finseq_1/T38')" onmouseout="rh()">FINSEQ_1:38</a></span>;<br/>
<a NAME="E13:56"/><span class="kw">then </span>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T25" onmouseover="rs('zfmisc_1/T25')" onmouseout="rh()">ZFMISC_1:25</a></span>;<br/>
<a NAME="E14:56"/><span class="kw">then </span>
 <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <font color="Maroon" title="c3">FF</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#D4" onmouseover="rs('card_3/D4')" onmouseout="rh()">CARD_3:def 4</a>, <a class="txt" href="#E11:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a></span>;<br/>
<a NAME="E15:56"/><span class="kw">then </span>
 <a href="matrix_0.html#K9" title="MATRIX_0:func.9">Values</a> <font color="Maroon" title="c3">FF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D9" onmouseover="rs('matrix_0/D9')" onmouseout="rh()">MATRIX_0:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:56"/>
<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> is    <a href="flexary1.html#M1" title="FLEXARY1:mode.1">DoubleReorganization</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="flexary1.html#D7" target="_self" onmouseover="rs('flexary1/D7')" onmouseout="rh()">Def7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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