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<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c6">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 4</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"> (  not <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> or  not <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> or  not <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x2</font> or <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:139_1_1"/><span class="lab"><font color="Green" title="E88">A1</font></span>: 
( <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> &amp; <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> )
 <span class="kw">and </span><br/><a NAME="E2:139_1_1"/><span class="lab"><font color="Green" title="E89">A2</font></span>: 
<span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x2</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="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">x1</font> = <font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c8">x2</font> = <font color="Maroon" title="c6">x2</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:139_1_1"><span class="lab"><font color="Green" title="E88">A1</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="139_1_1_1"><span class="kw">now </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">  not <font color="Maroon" title="c7">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">x2</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:139_1_1_1"/>
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">x2</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"> contradiction</span><br/><a NAME="E2:139_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c7">x1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">x2</font> or <font color="Maroon" title="c8">x2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">x1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><a NAME="E3:139_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c7">x1</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">x2</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="number14.html#K10" title="NUMBER14:func.10">exampleSierpinski150</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">D</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c7">x1</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#T98" target="_self" onmouseover="rs('number14/T98')" onmouseout="rh()">Th98</a></span>;<br/><span class="kw">hence </span><a NAME="E4:139_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:139_1_1"><span class="lab"><font color="Green" title="E89">A2</font></span></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:139_1_1"/>
<font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x2</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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