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<div class="add">

<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/>



<b>thus </b><a NAME="E1:35"/>
( <font color="Maroon" title="c1">seq1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font> implies for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</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">n</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c1">seq1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<a NAME="E2:35_1"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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/>
<b>hence </b><a NAME="E3:35_1"/>
<font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</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">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="seq_1.html#E1:35_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="seq_1.html#D7" target="_self" title="SEQ_1:def.7">Def7</a></i>;<br/>


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

<b>assume </b><a NAME="E2:35"/><i><font color="Green" title="E16">A2</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</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">n</font></span>)</span>
 ;<br/>

<i><font color="Green" title="E17">A3</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c1">seq1</font> = 
 <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="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">seq2</font>
<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="E4:35"/>
for <font color="Olive" title="b1">n</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">n</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> <font color="Maroon" title="c1">seq1</font> holds <br/><font color="Maroon" title="c1">seq1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</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">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="seq_1.html#E2:35"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:35"/>
<font color="Maroon" title="c1">seq1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="seq_1.html#K17" title="SEQ_1:func.17">-</a> <font color="Maroon" title="c2">seq2</font>
 <b>by </b><i><a class="txt" href="seq_1.html#E3:35"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="seq_1.html#D7" target="_self" title="SEQ_1:def.7">Def7</a></i>;<br/>


</div>
