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<b>let </b><font color="Maroon" title="c1">I</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> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="pralg_2.html#M2" title="PRALG_2:mode.2">MSAlgebra-Family</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>









<b>assume </b><a NAME="E1:34"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K3" title="PRALG_2:func.3">Frege</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pralg_2.html#K13" title="PRALG_2:func.13">?.</a> <font color="Maroon" title="c4">o</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:34"/><b>then </b>
 ex <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K3" title="PRALG_2:func.3">Frege</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pralg_2.html#K13" title="PRALG_2:func.13">?.</a> <font color="Maroon" title="c4">o</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pralg_2.html#K3" title="PRALG_2:func.3">Frege</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pralg_2.html#K13" title="PRALG_2:func.13">?.</a> <font color="Maroon" title="c4">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:34"/>
<font color="Maroon" title="c5">x</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 ;<br/>


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