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

<b>let </b><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</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">OU0</font> being  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">A</font> being   <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Olive" title="b1">OU0</font> holds   <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Olive" title="b1">OU0</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Olive" title="b1">OU0</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">OU0</font> be   <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</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">A</font> being   <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font> holds   <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span><br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">i</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"> ( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> implies <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/><b>assume </b><a NAME="E1:25_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</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"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/><b>then reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">i</font> as   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> ;<br/><b>set </b><font color="Maroon" title="c6">c1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> ;<br/><b>set </b><font color="Maroon" title="c7">c2</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> ;<br/><a NAME="E3:25_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s1</font></span>)</span> where <font color="Olive" title="b2">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b2">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  iff <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b2">s1</font></span>)</span> where <font color="Olive" title="b2">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b2">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</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"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  iff <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  implies <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  )</span>
<div class="add"><b>assume </b><a NAME="E1:25_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> </span><br/><b>then consider </b><font color="Maroon" title="c9">s1</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font><b> such that </b><br/><a NAME="E3:25_1_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s1</font> &amp; <font color="Maroon" title="c9">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> )
 ;<br/><a NAME="E4:25_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c9">s1</font> &amp; <font color="Maroon" title="c9">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> )
 <b>by </b><i><a class="txt" href="osalg_2.html#E3:25_1_1_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="msualg_2.html#D5" title="MSUALG_2:def.5">MSUALG_2:def 5</a></i>;<br/><b>hence </b><a NAME="E5:25_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> 
 ; <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>

<b>assume </b><a NAME="E2:25_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c9">s1</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font><b> such that </b><br/><a NAME="E4:25_1_1"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c9">s1</font> &amp; <font color="Maroon" title="c9">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> )
 ;<br/>
<a NAME="E5:25_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s1</font> &amp; <font color="Maroon" title="c9">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> )
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:25_1_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="msualg_2.html#D5" title="MSUALG_2:def.5">MSUALG_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:25_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> 
 ; <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="E4:25_1"/><b>then </b><i><font color="Green" title="E15">A3</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font></span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">s</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/><span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> = 
 <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> <font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c5">s</font>
<b>by </b><i><a class="ref" href="osalg_2.html#D5" target="_self" title="OSALG_2:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font>
<b>by </b><i><a class="txt" href="osalg_2.html#E4:25_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="osalg_2.html#D4" target="_self" title="OSALG_2:def.4">Def4</a></i>
;<br/><b>hence </b><a NAME="E6:25_1"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 ; <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="E2:25"/><b>then </b>
( ( for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> holds <br/><span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> holds <br/><span class="p1">(<span class="default"><a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p2">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) )
 
;<br/>
<a NAME="E3:25"/><b>then </b>
(  <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> &amp;  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D5" title="PBOOLE:def.5">PBOOLE:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
 <a href="osalg_2.html#K3" title="OSALG_2:func.3">OSConstants</a> <font color="Maroon" title="c2">OU0</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K2" title="MSUALG_2:func.2">Constants</a> <font color="Maroon" title="c2">OU0</font></span>)</span>
 <b>by </b><i><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>
