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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">z</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> holds   <a href="osalg_1.html#K5" title="OSALG_1:func.5">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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">CH</font> being   <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> holds   <a href="osalg_1.html#K5" title="OSALG_1:func.5">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/><span class="kw">let </span><font color="Maroon" title="c3">CH</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>,<span class="p1">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="osalg_1.html#K5" title="OSALG_1:func.5">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K5" title="OSALG_1:func.5">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#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D20" target="_self" title="OSALG_1:def.20">Def20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:60"/>
 <a href="osalg_1.html#K5" title="OSALG_1:func.5">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 class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T17" target="_self" title="OSALG_1:th.17">Th17</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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