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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">U0</font> being  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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/> for <font color="Olive" title="b2">U1</font>, <font color="Olive" title="b3">U2</font> being  <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Olive" title="b1">U0</font> holds  <font color="Olive" title="b2">U1</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Olive" title="b3">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">U2</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Olive" title="b2">U1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U0</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">U1</font>, <font color="Olive" title="b2">U2</font> being  <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font> holds  <font color="Olive" title="b1">U1</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Olive" title="b2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">U2</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Olive" title="b1">U1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">U1</font>, <font color="Maroon" title="c4">U2</font> be   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">U1</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c4">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">U2</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c5">u1</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">U1</font>, <font color="Maroon" title="c6">u2</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">U2</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></span>;<br/>
<a NAME="E2:71"/>
( <font color="Maroon" title="c5">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font> &amp; <font color="Maroon" title="c6">u2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E3:71"/><span class="kw">then </span>
<font color="Maroon" title="c5">u1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">A1</font> = <font color="Maroon" title="c5">u1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c6">u2</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E5:71"/>
( <font color="Maroon" title="c5">u1</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c6">u2</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T17" title="OSALG_1:th.17">OSALG_1:17</a></span>;<br/>
<a NAME="E6:71"/><span class="kw">then </span>
<font color="Maroon" title="c7">A1</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#T2" target="_self" title="OSALG_2:th.2">Th2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">A</font> = <font color="Maroon" title="c7">A1</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></span>;<br/>
<a NAME="E8:71"/>
<font color="Maroon" title="c3">U1</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c4">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c8">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D14" target="_self" title="OSALG_2:def.14">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:71"/>
<font color="Maroon" title="c3">U1</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c4">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">U2</font> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D14" target="_self" title="OSALG_2:def.14">Def14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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