<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: INTERVA1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A1</font>, <font color="Olive" title="b3">A2</font>, <font color="Olive" title="b4">B1</font>, <font color="Olive" title="b5">B2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">U</font>  st <font color="Olive" title="b2">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">A2</font> &amp; <font color="Olive" title="b4">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">B2</font> holds <br/> <a href="setfam_1.html#K3" title="SETFAM_1:func.3">INTERSECTION</a> (<span class="p1">(<span class="default"><a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> (<font color="Olive" title="b2">A1</font>,<font color="Olive" title="b3">A2</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> (<font color="Olive" title="b4">B1</font>,<font color="Olive" title="b5">B2</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">C</font> where <font color="Olive" title="b6">C</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">U</font> : ( <font color="Olive" title="b2">A1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b4">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">C</font> &amp; <font color="Olive" title="b6">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">A2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b5">B2</font> ) </span> } </span> </div></div>
