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<span class="kw">let </span><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b1">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Olive" title="b2">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) holds <br/><font color="Olive" title="b1">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">g</font> &amp; <font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) implies <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) )</span><br/>





<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">g</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) or  not <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) or <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E2:16"/>
( <font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span><br/>

<a NAME="E3:16"/><span class="kw">then </span>
( <font color="Maroon" title="c3">f</font> is   <a href="nomin_1.html#NM1" title="NOMIN_1:NM.1">NominativeSet</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">g</font> is   <a href="nomin_1.html#NM1" title="NOMIN_1:NM.1">NominativeSet</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#T4" target="_self" onmouseover="rs('nomin_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E4:16"/><span class="kw">then </span>
( <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> is <font color="Maroon" title="c1">V</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  &amp; <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> is <font color="Maroon" title="c2">A</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  )
 
;<br/>
<a NAME="E5:16"/><span class="kw">then </span>
<font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a>, <a class="ref" href="partfun1.html#T51" onmouseover="rs('partfun1/T51')" onmouseout="rh()">PARTFUN1:51</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:16"/>
<font color="Maroon" title="c3">f</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="nomin_1.html#K1" title="NOMIN_1:func.1">NDSS</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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