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<span class="kw">let </span><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#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">A</font> being    <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/>  for <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">A</font> holds <br/> <a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">i</font>,<font color="Olive" title="b3">x</font>) is    <a href="hallmar1.html#M2" title="HALLMAR1:mode.2">Reduction</a> of <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><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>; <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">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> (<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">x</font>) is    <a href="hallmar1.html#M2" title="HALLMAR1:mode.2">Reduction</a> of <font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><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#NK1" title="NUMBERS:NK.1">NAT</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">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Maroon" title="c3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> holds <br/> <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="Olive" title="b1">x</font>) is    <a href="hallmar1.html#M2" title="HALLMAR1:mode.2">Reduction</a> of <font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">x</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"> ( <font color="Maroon" title="c3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> implies  <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> )</span><br/>







<span class="kw">assume </span><a NAME="E1:35"/>
<font color="Maroon" title="c3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <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">  <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></span><br/>

<a NAME="E2:35"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hallmar1.html#T20" target="_self" onmouseover="rs('hallmar1/T20')" onmouseout="rh()">Th20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:35"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hallmar1.html#T19" target="_self" onmouseover="rs('hallmar1/T19')" onmouseout="rh()">Th19</a></span>; <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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