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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="compos_1.html#L1" title="COMPOS_1:struct.1">COM-Struct</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">I</font> being   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">loc</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">loc</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> <font color="Olive" title="b1">I</font> holds <br/><font color="Olive" title="b2">loc</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#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <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">  for <font color="Olive" title="b1">loc</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">loc</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> <font color="Maroon" title="c2">I</font> holds <br/><font color="Olive" title="b1">loc</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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">loc</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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"> ( <font color="Maroon" title="c3">loc</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> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c3">loc</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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c2">I</font></span>)</span> )</span><br/>





<a NAME="E1:107"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">I</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T21" onmouseover="rs('afinsq_1/T21')" onmouseout="rh()">AFINSQ_1:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:107"/>
( <font color="Maroon" title="c3">loc</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> <font color="Maroon" title="c2">I</font> implies <font color="Maroon" title="c3">loc</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#K10" title="COMPOS_1:func.10">stop</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"> verum</span><br/>


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