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<b>let </b><font color="Maroon" title="c1">seq1</font>, <font color="Maroon" title="c2">seq2</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>



<i><font color="Green" title="E17">A1</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span></span>)</span> = 
<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">seq2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c1">seq1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">seq2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<a NAME="E2:36"/>
for <font color="Olive" title="b1">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36_2"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span></span>)</span>
 ;<br/>

<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T11" target="_self" title="SEQ_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">seq2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="seq_1.html#E1:36_2"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="seq_1.html#T14" target="_self" title="SEQ_1:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">c</font></span>)</span>

;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:36"/>
<font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <font color="Maroon" title="c2">seq2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font></span>)</span>
 <b>by </b><i><a class="txt" href="seq_1.html#E1:36"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="seq_1.html#D4" target="_self" title="SEQ_1:def.4">Def4</a></i>;<br/>


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