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<b>let </b><font color="Maroon" title="c1">S0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>reconsider </b><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> <b>by </b><i><a class="ref" href="osalg_1.html#D6" title="OSALG_1:def.6">OSALG_1:def 6</a></i>;<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>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D3" title="MSUALG_2:def.3">MSUALG_2:def 3</a></i>;<br/>
<b>then consider </b><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="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S0</font><b> such that </b><br/><a NAME="E4:8"/><i><font color="Green" title="E6">A1</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">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#U3" title="MSUALG_1:sel.3">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> )
 <b>by </b><i><a class="ref" href="msualg_2.html#D2" title="MSUALG_2:def.2">MSUALG_2:def 2</a></i>;<br/>
<a NAME="E5:8"/>
( <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="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</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> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">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#U3" title="MSUALG_1:sel.3">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> )
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:8"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="osalg_1.html#D6" title="OSALG_1:def.6">OSALG_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E6:8"/>
<font color="Maroon" title="c2">s</font> is <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a>
 <b>by </b><i><a class="ref" href="msualg_2.html#D2" title="MSUALG_2:def.2">MSUALG_2:def 2</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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