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<span class="kw">set </span><font color="Maroon" title="c3">g</font> =  <a href="fomodel0.html#K5" title="FOMODEL0:func.5">MultPlace</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">f</font> = <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>;<br/>
<a NAME="E1:60_1_1"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="fomodel0.html#K5" title="FOMODEL0:func.5">MultPlace</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:60_1_1"/><span class="kw">then </span>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <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="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:60_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A1</font></span>: 
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <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="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="fomodel0.html#K5" title="FOMODEL0:func.5">MultPlace</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E4:60_1_1"/>
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  <a href="fomodel0.html#K5" title="FOMODEL0:func.5">MultPlace</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel0.html#E41"><span class="lab"><font color="Green" title="E36">Lm9</font></span></a></span>;<br/>
<a NAME="E5:60_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">D</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fomodel0.html#K5" title="FOMODEL0:func.5">MultPlace</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T34" title="FUNCT_4:th.34">FUNCT_4:34</a></span>;<br/>
<a NAME="E6:60_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:60_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">e</font> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>; <a class="txt" 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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