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<a NAME="E1:10_2_1"/>
(  ex <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  ) &amp;  ex <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E7">A6</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">q</font></span>)</span> = 
<font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D7" target="_self" title="BVFUNC_1:def.7">Def10</a></span>
<br/>.= 
<font color="Maroon" title="c1">A</font>

;<br/>
<a NAME="E3:10_2_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D16" title="MARGREL1:def.16">MARGREL1:def 16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:10_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">q</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">A</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_1"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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