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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c4">q3</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:69_1_1"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c2">A</font>
 ;<br/><a NAME="E2:69_1_1"/><b>then </b><i><font color="Green" title="E48">A2</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></i>;<br/><a NAME="E3:69_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:69_1_1"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="pscomp_1.html#D17" target="_self" title="PSCOMP_1:def.17">Def17</a></i>;<br/><a NAME="E4:69_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:69_1_1"><i><font color="Green" title="E48">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E5:69_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E1:69_1_1"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:69_1"/><i><font color="Green" title="E47">A3</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font></span>)</span>
 ;<br/><a NAME="E3:69_1"/><b>then </b><i><font color="Green" title="E48">A4</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></i>;<br/><a NAME="E4:69_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:69_1"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="pscomp_1.html#D17" target="_self" title="PSCOMP_1:def.17">Def17</a></i>;<br/><a NAME="E5:69_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">q3</font> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:69_1"><i><font color="Green" title="E48">A4</font></i></a></i>;<br/><a NAME="E6:69_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T22" target="_self" title="PSCOMP_1:th.22">Th22</a></i>;<br/><a NAME="E7:69_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T21" target="_self" title="PSCOMP_1:th.21">Th21</a></i>;<br/><b>hence </b><a NAME="E8:69_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E2:69_1"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:69"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">q3</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">+</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">q3</font></span>)</span> <a href="measure6.html#K6" title="MEASURE6:func.6">++</a> <font color="Maroon" title="c2">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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