<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font> be    <a href="seqfunc.html#M1" title="SEQFUNC:mode.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c4">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E36">A1</font></i>: 
( <font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font> &amp; <font color="Maroon" title="c3">H2</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font> )
 ;<br/>

<a NAME="E2:51"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c4">X</font> <a href="seqfunc.html#R1" title="SEQFUNC:pred.1">common_on_dom</a> <font color="Maroon" title="c2">H1</font>
 
<b>by </b><i><a class="ref" href="seqfunc.html#D12" target="_self" title="SEQFUNC:def.12">Def12</a></i>;<br/>
<a NAME="E3:51"/>
<font color="Maroon" title="c4">X</font> <a href="seqfunc.html#R1" title="SEQFUNC:pred.1">common_on_dom</a> <font color="Maroon" title="c3">H2</font>
 
<b>by </b><i><a class="txt" href="seqfunc.html#E1:51"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="seqfunc.html#D12" target="_self" title="SEQFUNC:def.12">Def12</a></i>;<br/>
<b>hence </b><a NAME="E4:51"/>
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> holds <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H2</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K6" title="SEQFUNC:func.6">+</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H2</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K7" title="SEQFUNC:func.7">-</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H2</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="seqfunc.html#K8" title="SEQFUNC:func.8">(#)</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b1">x</font> )
 <b>by </b><i><a class="txt" href="seqfunc.html#E2:51"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="seqfunc.html#T32" target="_self" title="SEQFUNC:th.32">Th32</a></i>;<br/>


</div>
