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<b>let </b><font color="Maroon" title="c1">S</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">z</font> being 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> <br/> for <font color="Olive" title="b2">CH</font> being   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">z</font></span>)</span> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">z</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> holds   <a href="osalg_1.html#K6" title="OSALG_1:func.6">ConstOSA</a> <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">z</font>,<font color="Olive" title="b2">CH</font> is <a href="osalg_1.html#V12" title="OSALG_1:attr.12">order-sorted</a></span><br/><b>let </b><font color="Maroon" title="c2">z</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">CH</font> being   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> holds   <a href="osalg_1.html#K6" title="OSALG_1:func.6">ConstOSA</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>,<font color="Olive" title="b1">CH</font> is <a href="osalg_1.html#V12" title="OSALG_1:attr.12">order-sorted</a></span><br/><b>let </b><font color="Maroon" title="c3">CH</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="osalg_1.html#K6" title="OSALG_1:func.6">ConstOSA</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">CH</font> is <a href="osalg_1.html#V12" title="OSALG_1:attr.12">order-sorted</a></span><br/>





<a NAME="E1:60"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K6" title="OSALG_1:func.6">ConstOSA</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">CH</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_1.html#K5" title="OSALG_1:func.5">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#D20" target="_self" title="OSALG_1:def.20">Def20</a></i>;<br/>
<b>hence </b><a NAME="E2:60"/>
 <a href="osalg_1.html#K6" title="OSALG_1:func.6">ConstOSA</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">CH</font> is <a href="osalg_1.html#V12" title="OSALG_1:attr.12">order-sorted</a>
 <b>by </b><i><a class="ref" href="osalg_1.html#T17" target="_self" title="OSALG_1:th.17">Th17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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