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<span class="kw">let </span><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font> be   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of ; <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="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">sI</font> =  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">sIJ</font> =  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span>;<br/>
<span class="lab"><font color="Green" title="E4">A1</font></span>:  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></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"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_5.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="afinsq_1.html#T17" onmouseover="rs('afinsq_1/T17')" onmouseout="rh()">AFINSQ_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" onmouseover="rs('afinsq_1/T17')" onmouseout="rh()">AFINSQ_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">J</font></span>)</span>

;<br/>
<a NAME="E2:13"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_5.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="afinsq_1.html#T17" onmouseover="rs('afinsq_1/T17')" onmouseout="rh()">AFINSQ_1:17</a></span>;<br/>
<a NAME="E3:13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">A</font> =  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">x</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="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN: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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN: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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:13"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN: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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN: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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span></span><br/>

<a NAME="E5:13"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" onmouseover="rs('relat_1/D18')" onmouseout="rh()">RELAT_1:def 18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">l</font> = <font color="Maroon" title="c6">x</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13"><span class="lab"><font color="Green" title="E6">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">n</font> = <font color="Maroon" title="c7">l</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<a NAME="E8:13"/>
<font color="Maroon" title="c8">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c1">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>;<br/>
<a NAME="E9:13"/><span class="kw">then </span>
<font color="Maroon" title="c8">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:13"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN: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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">';'</a> <font color="Maroon" title="c2">J</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</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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