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<a NAME="E1:11_1_1"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">seq</font> <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/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_1_1_1"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ;<br/><b>consider </b><font color="Maroon" title="c2">n0</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> ;<br/><b>reconsider </b><font color="Maroon" title="c3">r</font> = <font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c2">n0</font> as  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  ;<br/><b>take </b><font color="Maroon" title="c4">r</font> = <font color="Maroon" title="c3">r</font>;<br/><b>let </b><font color="Maroon" title="c5">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/><b>thus </b><a NAME="E4:11_1_1_1"/>
<font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E1:11_1_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="seqm_3.html#E1:11_1_1_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c2">r</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><a NAME="E4:11_1_1"/><i><font color="Green" title="E15">A3</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">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">n1</font>, <font color="Maroon" title="c4">n2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a><br/>

<b>assume </b><a NAME="E5:11_1_1"/><i><font color="Green" title="E16">A4</font></i>: 
( <font color="Maroon" title="c3">n1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">seq</font> &amp; <font color="Maroon" title="c4">n2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">seq</font> )
 ;<br/>

<b>hence </b><font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">n1</font> = 
<font color="Maroon" title="c2">r</font>
<b>by </b><i><a class="txt" href="seqm_3.html#E1:11_1_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="seqm_3.html#E4:11_1_1"><i><font color="Green" title="E15">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">n2</font>
<b>by </b><i><a class="txt" href="seqm_3.html#E1:11_1_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="seqm_3.html#E4:11_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="seqm_3.html#E5:11_1_1"><i><font color="Green" title="E16">A4</font></i></a></i>
;<br/><br/>


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