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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>thus </b><a NAME="E1:7"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:7_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">r</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E3:7_1"/>
 <a href="real_1.html#K1">-</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun3.html#K6">-</a> <span class="p2">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:7_1"/><b>then </b>
 <a href="real_1.html#K1">-</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#T36">SEQ_1:36</a></i>;<br/>
<a NAME="E5:7_1"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">r</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pscomp_1.html#T14">PSCOMP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E6:7_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:7"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">r</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E4:7"/>
 <a href="real_1.html#K1">-</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K4">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K4">-</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T14">PSCOMP_1:14</a></i>;<br/>
<a NAME="E5:7"/><b>then </b>
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">r</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun3.html#K6">-</a> <font color="Maroon">seq</font></span>)</span>
 ;<br/>


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