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<b>let </b><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon" title="c2">U0</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="osalg_2.html#K13" title="OSALG_2:func.13">OSSub</a> <font color="Maroon" title="c2">U0</font>;<br/>





<a NAME="E1:76"/>
( <font color="Maroon" title="c3">x</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font> &amp; <font color="Maroon" title="c4">y</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font> )
 
<b>by </b><i><a class="ref" href="osalg_2.html#D15" target="_self" title="OSALG_2:def.15">Def15</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">U1</font>, <font color="Maroon" title="c6">U2</font> being  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font><b> such that </b><br/><a NAME="E3:76"/><i><font color="Green" title="E51">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">U1</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">U2</font> )
 ;<br/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K15" title="OSALG_2:func.15">OSAlg_meet</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> = 
<font color="Maroon" title="c5">U1</font> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <font color="Maroon" title="c6">U2</font>
<b>by </b><i><a class="txt" href="osalg_2.html#E3:76"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="osalg_2.html#D17" target="_self" title="OSALG_2:def.17">Def17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_2.html#K16" title="MSUALG_2:func.16">MSAlg_meet</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="txt" href="osalg_2.html#E3:76"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="msualg_2.html#D22" title="MSUALG_2:def.22">MSUALG_2:def 22</a></i>
;<br/>
<b>hence </b><a NAME="E5:76"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K15" title="OSALG_2:func.15">OSAlg_meet</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K16" title="MSUALG_2:func.16">MSAlg_meet</a> <font color="Maroon" title="c2">U0</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>
 ;<br/>


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