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<span class="kw">set </span><font color="Maroon" title="c5">X</font> =  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Y</font> =  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 ex <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" onmouseover="rs('funct_2/D2')" onmouseout="rh()">FUNCT_2:def 2</a></span>;<br/>
<a NAME="E2:14_1_1"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">s</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T8" onmouseover="rs('funcop_1/T8')" onmouseout="rh()">FUNCOP_1:8</a></span>;<br/>
<a NAME="E3:14_1_1"/><span class="kw">then </span>
(  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="funct_4.html#T17" onmouseover="rs('funct_4/T17')" onmouseout="rh()">FUNCT_4:17</a>, <a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</a></span>;<br/>
<a NAME="E4:14_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A2</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<a NAME="E5:14_1_1"/><span class="lab"><font color="Green" title="E8">A3</font></span>: 
<font color="Maroon" title="c3">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" onmouseover="rs('int_1/D2')" onmouseout="rh()">INT_1:def 2</a></span>;<br/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" onmouseover="rs('funct_4/D1')" onmouseout="rh()">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>

<br/>.= 
 <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T40" onmouseover="rs('zfmisc_1/T40')" onmouseout="rh()">ZFMISC_1:40</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1"/>
<font color="Maroon" title="c2">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> is   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="funct_2.html#D2" onmouseover="rs('funct_2/D2')" onmouseout="rh()">FUNCT_2:def 2</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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