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<span class="kw">let </span><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> holds   <a href="osalg_2.html#K12" title="OSALG_2:func.12">OSSub</a> <font color="Olive" title="b1">OU0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_2.html#K14" title="MSUALG_2:func.14">MSSub</a> <font color="Olive" title="b1">OU0</font></span><br/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="osalg_2.html#K12" title="OSALG_2:func.12">OSSub</a> <font color="Maroon" title="c2">OU0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_2.html#K14" title="MSUALG_2:func.14">MSSub</a> <font color="Maroon" title="c2">OU0</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="osalg_2.html#K12" title="OSALG_2:func.12">OSSub</a> <font color="Maroon" title="c2">OU0</font> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_2.html#K14" title="MSUALG_2:func.14">MSSub</a> <font color="Maroon" title="c2">OU0</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:70"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="osalg_2.html#K12" title="OSALG_2:func.12">OSSub</a> <font color="Maroon" title="c2">OU0</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_2.html#K14" title="MSUALG_2:func.14">MSSub</a> <font color="Maroon" title="c2">OU0</font></span><br/>

<a NAME="E2:70"/><span class="kw">then </span>
<font color="Maroon" title="c3">x</font> is   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">OU0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D14" target="_self" onmouseover="rs('osalg_2/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:70"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msualg_2.html#K14" title="MSUALG_2:func.14">MSSub</a> <font color="Maroon" title="c2">OU0</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D19" onmouseover="rs('msualg_2/D19')" onmouseout="rh()">MSUALG_2:def 19</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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