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<span class="lab"><font color="Green" title="E1">A1</font></span>:  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" onmouseover="rs('afinsq_1/T70')" onmouseout="rh()">AFINSQ_1:70</a></span>
<br/>.= 
2 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T56" onmouseover="rs('compos_1/T56')" onmouseout="rh()">COMPOS_1:56</a></span>
<br/>.= 
2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>
<br/>.= 
1

;<br/>
<span class="kw">hence </span><a NAME="E2:3_1_1"/>
<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p2">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T59" onmouseover="rs('compos_1/T59')" onmouseout="rh()">COMPOS_1:59</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D14" onmouseover="rs('compos_1/D14')" onmouseout="rh()">COMPOS_1:def 14</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">  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font> is  <a href="compos_1.html#V4" title="COMPOS_1:attr.4">unique-halt</a> </span><br/>

<span class="kw">thus </span><a NAME="E3:3_1_1"/>
 <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font> is  <a href="compos_1.html#V4" title="COMPOS_1:attr.4">unique-halt</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"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="3_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D15" onmouseover="rs('compos_1/D15')" onmouseout="rh()">COMPOS_1:def 15</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 <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</font> or  not <font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> or <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:3_1_1_2"/><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c1">S</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="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> or <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:3_1_1_2"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</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"> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="3_1_1_2_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="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:3_1_1_2_1"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> contradiction</span><br/><a NAME="E2:3_1_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T58" onmouseover="rs('compos_1/T58')" onmouseout="rh()">COMPOS_1:58</a></span>;<br/><span class="kw">hence </span><a NAME="E3:3_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1_2"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="compos_0.html#D12" onmouseover="rs('compos_0/D12')" onmouseout="rh()">COMPOS_0:def 12</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="E4:3_1_1_2"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K62" title="VALUED_1:func.62">LastLoc</a> <span class="p1">(<span class="default"><a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:3_1_1_2"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="txt" href="#E1:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="compos_1.html#T60" onmouseover="rs('compos_1/T60')" onmouseout="rh()">COMPOS_1:60</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>


</div>
