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<b>let </b><font color="Maroon" title="c1">F</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <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="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:33"/>
( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> )
 ;<br/>

<a NAME="E2:33"/><b>then </b>
 <a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font> is    <a href="hallmar1.html#M1" title="HALLMAR1:mode.1">Reduction</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">i</font>
 
<b>by </b><i><a class="ref" href="hallmar1.html#T20" target="_self" title="HALLMAR1:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
 <a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font> is    <a href="hallmar1.html#M2" title="HALLMAR1:mode.2">Reduction</a> of <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="hallmar1.html#T19" target="_self" title="HALLMAR1:th.19">Th19</a></i>;<br/>


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