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

<b>let </b><font color="Maroon" title="c1">I</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> ; <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">M</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">EqR1</font>, <font color="Olive" title="b3">EqR2</font>, <font color="Olive" title="b4">EqR3</font> being  <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Olive" title="b1">M</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b3">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b4">EqR3</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b4">EqR3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</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"> for <font color="Olive" title="b1">EqR1</font>, <font color="Olive" title="b2">EqR2</font>, <font color="Olive" title="b3">EqR3</font> being  <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b2">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b3">EqR3</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b3">EqR3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">EqR1</font>, <font color="Maroon" title="c4">EqR2</font>, <font color="Maroon" title="c5">EqR3</font> be   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span></span><br/>









<a NAME="E1:14"/>
for <font color="Olive" title="b1">EqR4</font> being  <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> holds <br/><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">EqR4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">EqR4</font> be   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> implies <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> )</span><br/>

<a NAME="E1:14_1"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E2:14_1"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E3:14_1"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self" title="MSUALG_5:th.6">Th6</a></i>;<br/>
<a NAME="E4:14_1"/><i><font color="Green" title="E13">A4</font></i>: 
( <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> &amp; <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<b>assume </b><a NAME="E5:14_1"/>
<font color="Maroon" title="c6">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font></span><br/>

<a NAME="E6:14_1"/><b>then </b><i><font color="Green" title="E14">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self" title="MSUALG_5:th.6">Th6</a></i>;<br/>
<a NAME="E7:14_1"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E1:14_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E8:14_1"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E3:14_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E9:14_1"/><b>then </b><i><font color="Green" title="E15">A6</font></i>: 
( <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> &amp; <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> &amp; <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> )
 
<b>by </b><i><a class="txt" href="#E2:14_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="#E4:14_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E6:14_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E10:14_1"/><b>then </b>
<font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<a NAME="E11:14_1"/><b>then </b>
<font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T7" target="_self" title="MSUALG_5:th.7">Th7</a></i>;<br/>
<a NAME="E12:14_1"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E9:14_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<b>hence </b><a NAME="E13:14_1"/>
<font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 <b>by </b><i><a class="ref" href="msualg_5.html#T7" target="_self" title="MSUALG_5:th.7">Th7</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><b>end;</b></div>
<a NAME="E2:14"/><b>then </b><i><font color="Green" title="E10">A7</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font>
 
;<br/>
<a NAME="E3:14"/>
for <font color="Olive" title="b1">EqR4</font> being  <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">EqR4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">EqR4</font> be   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> )</span><br/>

<a NAME="E1:14_2"/><i><font color="Green" title="E11">A8</font></i>: 
<font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E2:14_2"/><i><font color="Green" title="E12">A9</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E3:14_2"/><i><font color="Green" title="E13">A10</font></i>: 
<font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self" title="MSUALG_5:th.6">Th6</a></i>;<br/>
<a NAME="E4:14_2"/><i><font color="Green" title="E14">A11</font></i>: 
( <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> &amp; <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<b>assume </b><a NAME="E5:14_2"/>
<font color="Maroon" title="c6">EqR4</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font></span><br/>

<a NAME="E6:14_2"/><b>then </b><i><font color="Green" title="E15">A12</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self" title="MSUALG_5:th.6">Th6</a></i>;<br/>
<a NAME="E7:14_2"/><b>then </b>
<font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E1:14_2"><i><font color="Green" title="E11">A8</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E8:14_2"/><b>then </b>
<font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E3:14_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E9:14_2"/><b>then </b><i><font color="Green" title="E16">A13</font></i>: 
( <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> &amp; <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> &amp; <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font> )
 
<b>by </b><i><a class="txt" href="#E2:14_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="#E4:14_2"><i><font color="Green" title="E14">A11</font></i></a>, <a class="txt" href="#E6:14_2"><i><font color="Green" title="E15">A12</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E10:14_2"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<a NAME="E11:14_2"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T7" target="_self" title="MSUALG_5:th.7">Th7</a></i>;<br/>
<a NAME="E12:14_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 
<b>by </b><i><a class="txt" href="#E9:14_2"><i><font color="Green" title="E16">A13</font></i></a>, <a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<b>hence </b><a NAME="E13:14_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c6">EqR4</font>
 <b>by </b><i><a class="ref" href="msualg_5.html#T7" target="_self" title="MSUALG_5:th.7">Th7</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><b>end;</b></div>
<a NAME="E4:14"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:14"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">EqR2</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c5">EqR3</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:14"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</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>
