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

<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">G</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">sf</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">I</font>  st <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">sf</font> holds <br/> <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Olive" title="b1">sf</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font></span><br/><b>let </b><font color="Maroon" title="c3">sf</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">sf</font> implies  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c3">sf</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font> )</span><br/>





<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">sf</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c3">sf</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font></span><br/>

<a NAME="E2:4"/><b>then </b>
 <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c3">sf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c3">sf</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>;<br/>
<b>hence </b><a NAME="E3:4"/>
 <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c3">sf</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:4"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="setfam_1.html#T4" title="SETFAM_1:th.4">SETFAM_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
