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<span class="kw">let </span><font color="Maroon" title="c1">S0</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>   <a href="msualg_2.html#V2" title="MSUALG_2:attr.2">all-with_const_op</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <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#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font> is  <a href="msualg_2.html#V2" title="MSUALG_2:attr.2">all-with_const_op</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="msualg_2.html#D3" title="MSUALG_2:def.3">MSUALG_2:def 3</a> <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="c2">s</font> is  <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> </span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">s1</font> = <font color="Maroon" title="c2">s</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D6" title="OSALG_1:def.6">OSALG_1:def 6</a></span>;<br/>
<a NAME="E2:8"/>
<font color="Maroon" title="c3">s1</font> is  <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D3" title="MSUALG_2:def.3">MSUALG_2:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">o</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S0</font><span class="kw"> such that </span><br/><a NAME="E4:8"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D2" title="MSUALG_2:def.2">MSUALG_2:def 2</a></span>;<br/>
<a NAME="E5:8"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c4">o</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D6" title="OSALG_1:def.6">OSALG_1:def 6</a></span>;<br/>
<a NAME="E6:8"/>
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="osalg_1.html#D6" title="OSALG_1:def.6">OSALG_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:8"/>
<font color="Maroon" title="c2">s</font> is  <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="msualg_2.html#D2" title="MSUALG_2:def.2">MSUALG_2:def 2</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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